https://peda.net/id/fff68c9cf51 2018-01-09T10:20:49+02:00 https://peda.net/:static/532/peda.net.logo.bg.svg <div class="license">Tämän sivun lisenssi <a rel="license" href="https://peda.net/info">Peda.net-yleislisenssi</a></div> https://peda.net/id/0088d462169 2018-02-21T00:50:58+02:00 <a href="https://peda.net/p/kirin_porsti/ma/ma3p/s-178-t-470/t-470-png2#top" title="T.470.PNG"><img src="https://peda.net/p/kirin_porsti/ma/ma3p/s-178-t-470/t-470-png2:file/photo/7a8b69d8674451f464a461f1bd3a7f837455866e/T.470.PNG" alt="" title="T.470.PNG" class="inline" loading="lazy"/></a><br/> a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Calpha%3D90-66%7B%2C%7D5%3D23%7B%2C%7D5%C2%B0" alt="\alpha=90-66{,}5=23{,}5°"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csin23%7B%2C%7D5%3D%5Cfrac%7Bx%7D%7B6371%7D" alt="\sin23{,}5=\frac{x}{6371}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D2540%7B%2C%7D430...%5Capprox2540%5Cleft(km%5Cright)" alt="x=2540{,}430...\approx2540\left(km\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=y%3D%5Csqrt%5B%5D%7B2540%5E2%2B2540%5E2%7D%3D3592%7B%2C%7D1024...%5Capprox3590%5Cleft(km%5Cright)" alt="y=\sqrt[]{2540^2+2540^2}=3592{,}1024...\approx3590\left(km\right)"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=2%5Cpi%5Ccdot2540%5Ccdot%5Cfrac%7B90%7D%7B360%7D%3D3989%7B%2C%7D822...%5Capprox3990%5Cleft(km%5Cright)" alt="2\pi\cdot2540\cdot\frac{90}{360}=3989{,}822...\approx3990\left(km\right)"/> 2018-02-21T00:47:17+02:00 https://peda.net/id/0927361a168 2018-02-21T00:33:12+02:00 a)<img src="https://math-demo.abitti.fi/math.svg?latex=V%3D%5Cfrac%7B%5Cfrac%7B4%7D%7B3%7D%5Cpi%5Ccdot%5Cleft(%5Cfrac%7B20%7D%7B2%7D%5Cright)%5E3%7D%7B2%7D%3D2094%7B%2C%7D395...%5Capprox2100%5Cleft(cm%5E3%5Cright)" alt="V=\frac{\frac{4}{3}\pi\cdot\left(\frac{20}{2}\right)^3}{2}=2094{,}395...\approx2100\left(cm^3\right)"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=A%3D%5Cfrac%7B4%5Cpi%5Ccdot%5Cleft(%5Cfrac%7B20%7D%7B2%7D%5Cright)%5E2%7D%7B2%7D%3D200%5Cpi%3D628%7B%2C%7D318...%5Capprox628%5Cleft(cm%5E2%5Cright)" alt="A=\frac{4\pi\cdot\left(\frac{20}{2}\right)^2}{2}=200\pi=628{,}318...\approx628\left(cm^2\right)"/><br/> c)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=2100%5Ccdot%5Cfrac%7B45%7D%7B360%7D%3D262%7B%2C%7D5%5Capprox260%5Cleft(cm%5E3%5Cright)" alt="2100\cdot\frac{45}{360}=262{,}5\approx260\left(cm^3\right)"/> 2018-02-21T00:33:12+02:00 https://peda.net/id/d7869a84168 2018-02-21T00:26:48+02:00 a)<br/> <a href="https://peda.net/p/kirin_porsti/ma/ma3p/s-177-t-465/t-465-a-png#top" title="T.465 a.PNG"><img src="https://peda.net/p/kirin_porsti/ma/ma3p/s-177-t-465/t-465-a-png:file/photo/193b77348fce6acddfb03f0e2397a3a77ce75bbc/T.465%20a.PNG" alt="" title="T.465 a.PNG" class="inline" loading="lazy"/></a><br/> b) <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B4%5E3%7D%7B%5Cfrac%7B4%7D%7B3%7D%5Cpi%5Ccdot2%5E3%7D%3D%5Cfrac%7B64%7D%7B%5Cfrac%7B32%7D%7B3%7D%5Cpi%7D%3D%5Cfrac%7B6%7D%7B%5Cpi%7D" alt="\frac{4^3}{\frac{4}{3}\pi\cdot2^3}=\frac{64}{\frac{32}{3}\pi}=\frac{6}{\pi}"/> 2018-02-21T00:24:40+02:00 https://peda.net/id/44b05322168 2018-02-21T00:15:24+02:00 <a href="https://peda.net/p/kirin_porsti/ma/ma3p/s-177-t-464/t-464-png#top" title="T.464.PNG"><img src="https://peda.net/p/kirin_porsti/ma/ma3p/s-177-t-464/t-464-png:file/photo/fdaa1e3c6cd2ca061cf579ddb6c8c29130482a7a/T.464.PNG" alt="" title="T.464.PNG" class="inline" loading="lazy"/></a><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Calpha%3D90-66%7B%2C%7D5%3D23%7B%2C%7D5%C2%B0" alt="\alpha=90-66{,}5=23{,}5°"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csin23%7B%2C%7D5%3D%5Cfrac%7Bx%7D%7B6370%7D" alt="\sin23{,}5=\frac{x}{6370}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D2540%7B%2C%7D031...%5Capprox2540%5Cleft(km%5Cright)" alt="x=2540{,}031...\approx2540\left(km\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=2%5Cpi%5Ccdot2540%3D5080%5Cpi%3D15959%7B%2C%7D290...%5Capprox16000%5Cleft(km%5Cright)" alt="2\pi\cdot2540=5080\pi=15959{,}290...\approx16000\left(km\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=V%3A%5C%20n.%5C%2016000km" alt="V:\ n.\ 16000km"/> 2018-02-21T00:13:24+02:00 https://peda.net/id/0771bb80167 2018-02-20T22:31:28+02:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=h%3D%5Csqrt%5B%5D%7B7%7B%2C%7D8%5E2-%5Cleft(%5Cfrac%7B6%7D%7B2%7D%5Cright)%5E2%7D" alt="h=\sqrt[]{7{,}8^2-\left(\frac{6}{2}\right)^2}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=h%3D7%7B%2C%7D2" alt="h=7{,}2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=V%3D%5Cfrac%7B1%7D%7B3%7D%5Ccdot%5Cpi%5Ccdot%5Cleft(%5Cfrac%7B6%7D%7B3%7D%5Cright)%5E2%5Ccdot7%7B%2C%7D2%3D67%7B%2C%7D858...%5Capprox68%5C%20%5Cleft(cm%5E2%5Cright)" alt="V=\frac{1}{3}\cdot\pi\cdot\left(\frac{6}{3}\right)^2\cdot7{,}2=67{,}858...\approx68\ \left(cm^2\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=A_p%3D%5Cleft(%5Cfrac%7B6%7D%7B2%7D%5Cright)%5E2%5Cpi%3D9%5Cpi28%7B%2C%7D274...%5Capprox28%5Cleft(cm%5E2%5Cright)" alt="A_p=\left(\frac{6}{2}\right)^2\pi=9\pi28{,}274...\approx28\left(cm^2\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=A_v%3D%5Cpi%5Ccdot%5Cfrac%7B6%7D%7B2%7D%3D7%7B%2C%7D8%3D73%7B%2C%7D513...%5Capprox74%5Cleft(cm%5E2%5Cright)" alt="A_v=\pi\cdot\frac{6}{2}=7{,}8=73{,}513...\approx74\left(cm^2\right)"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Csqrt%5B%5D%7B2%7B%2C%7D9%5E2-2%5E2%7D" alt="x=\sqrt[]{2{,}9^2-2^2}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D2%7B%2C%7D1" alt="x=2{,}1"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=h%3D%5Csqrt%5B%5D%7B2%7B%2C%7D1%5E2-2%5E2%7D" alt="h=\sqrt[]{2{,}1^2-2^2}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=h%3D0%7B%2C%7D640...%5Capprox0%7B%2C%7D64%5Cleft(cm%5Cright)" alt="h=0{,}640...\approx0{,}64\left(cm\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=V%3D4%5E2%5Ccdot0%7B%2C%7D64%5Ccdot%5Cfrac%7B1%7D%7B3%7D%3D3%7B%2C%7D4%5Cleft(cm%5E3%5Cright)" alt="V=4^2\cdot0{,}64\cdot\frac{1}{3}=3{,}4\left(cm^3\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=A_p%3D4%5E2%3D16%5Cleft(cm%5E2%5Cright)" alt="A_p=4^2=16\left(cm^2\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=A_v%3D2%7B%2C%7D1%5Ccdot4%5Ccdot2%3D16%7B%2C%7D8%5Capprox17%5Cleft(cm%5E2%5Cright)" alt="A_v=2{,}1\cdot4\cdot2=16{,}8\approx17\left(cm^2\right)"/> 2018-02-20T22:31:28+02:00 https://peda.net/id/541db3ec167 2018-02-20T22:16:48+02:00 <a href="https://peda.net/p/kirin_porsti/ma/ma3p/s-168-t-444/t-444-png#top" title="T.444.PNG"><img src="https://peda.net/p/kirin_porsti/ma/ma3p/s-168-t-444/t-444-png:file/photo/1306936864f6297fc4780ec306a80f15a5c16312/T.444.PNG" alt="" title="T.444.PNG" class="inline" loading="lazy"/></a><br/> <div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Csqrt%5B%5D%7B24%5E2%2B%5Cleft(%5Cfrac%7B25%7D%7B2%7D%5Cright)%5E2%7D%3D27%7B%2C%7D060...%5Capprox27%5Cleft(cm%5Cright)" alt="x=\sqrt[]{24^2+\left(\frac{25}{2}\right)^2}=27{,}060...\approx27\left(cm\right)"/></div> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=A_v%3D%5Cpi%5Ccdot12%7B%2C%7D5%5Ccdot27%3D1066%7B%2C%7D2875...%5Capprox1060%5Cleft(cm%5Cright)" alt="A_v=\pi\cdot12{,}5\cdot27=1066{,}2875...\approx1060\left(cm\right)"/></div> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=A_k%3D27%5E2%5Cpi%3D729%5Cpi" alt="A_k=27^2\pi=729\pi"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B1060%7D%7B729%5Cpi%7D%5Ccdot360%3D166%7B%2C%7D421...%5Capprox166%C2%B0" alt="\frac{1060}{729\pi}\cdot360=166{,}421...\approx166°"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=V%3A%5C%20Sektorin%5C%20s%C3%A4de%5C%20on%5C%20n.%5C%2027cm%5C%20ja%5C%20keskuskulma%5C%20n.166%C2%B0" alt="V:\ Sektorin\ säde\ on\ n.\ 27cm\ ja\ keskuskulma\ n.166°"/> 2018-02-20T22:12:08+02:00 https://peda.net/id/c8e0186a167 2018-02-20T22:08:27+02:00 <a href="https://peda.net/p/kirin_porsti/ma/ma3p/s-158-t-427/t-427-png#top" title="T.427.PNG"><img src="https://peda.net/p/kirin_porsti/ma/ma3p/s-158-t-427/t-427-png:file/photo/81e62412f2475690ed64207e44d3314db7f17b65/T.427.PNG" alt="" title="T.427.PNG" class="inline" loading="lazy"/></a><br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cpi%20x%5E2%3D1000%3A10" alt="\pi x^2=1000:10"/></div> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cpi%20x%3D100" alt="\pi x=100"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%3D31%7B%2C%7D8309..." alt="x^2=31{,}8309..."/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D5%7B%2C%7D6418...%5Capprox5%7B%2C%7D6%5Cleft(cm%5Cright)" alt="x=5{,}6418...\approx5{,}6\left(cm\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=2%5Cpi%20x%3D2%5Cpi%5Ccdot5%7B%2C%7D6%3D35%7B%2C%7D185...%5Capprox35%5Cleft(cm%5Cright)" alt="2\pi x=2\pi\cdot5{,}6=35{,}185...\approx35\left(cm\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=V%3A%5C%2035%5Ccdot10" alt="V:\ 35\cdot10"/> 2018-02-20T22:08:15+02:00 https://peda.net/id/9dcff538167 2018-02-20T21:59:53+02:00 <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B%5Cpi%5Ccdot7%5E2%5Ccdot14%7D%7B14%5E3%7D%3D0%7B%2C%7D7853...%5Capprox0%7B%2C%7D79%3D79%5C%25" alt="\frac{\pi\cdot7^2\cdot14}{14^3}=0{,}7853...\approx0{,}79=79\%"/></div> <img src="https://math-demo.abitti.fi/math.svg?latex=V%3A%5C%20n.%5C%2079%5C%25" alt="V:\ n.\ 79\%"/> 2018-02-20T21:59:53+02:00 https://peda.net/id/5dd2adc2167 2018-02-20T21:58:08+02:00 <a href="https://peda.net/p/kirin_porsti/ma/ma3p/s-149-t-408/t-408-png#top" title="T.408.PNG"><img src="https://peda.net/p/kirin_porsti/ma/ma3p/s-149-t-408/t-408-png:file/photo/9b2a713b49739ca489b2495028939c665ec30e9d/T.408.PNG" alt="" title="T.408.PNG" class="inline" loading="lazy"/></a> 2018-02-20T21:58:06+02:00 https://peda.net/id/27fb65b8167 2018-02-20T21:57:02+02:00 a)<br/> <a href="https://peda.net/p/kirin_porsti/ma/ma3p/s-148-t-405/t-405-a-png#top" title="T.405 a.PNG"><img src="https://peda.net/p/kirin_porsti/ma/ma3p/s-148-t-405/t-405-a-png:file/photo/703be78ebc8b52d6335ecdceb73eeb92a97ab112/T.405%20a.PNG" alt="" title="T.405 a.PNG" class="inline" loading="lazy"/></a><br/> b)<br/> <a href="https://peda.net/p/kirin_porsti/ma/ma3p/s-148-t-405/t-405-b-png#top" title="T.405 b.PNG"><img src="https://peda.net/p/kirin_porsti/ma/ma3p/s-148-t-405/t-405-b-png:file/photo/d283ecbceedc13fe148207cf2b209e0b1e7b174d/T.405%20b.PNG" alt="" title="T.405 b.PNG" class="inline" loading="lazy"/></a> 2018-02-20T21:56:35+02:00 https://peda.net/id/46f1ca58167 2018-02-20T21:52:31+02:00 <a href="https://peda.net/p/kirin_porsti/ma/ma3p/s-136-t-354/t-354-png#top" title="T.354.PNG"><img src="https://peda.net/p/kirin_porsti/ma/ma3p/s-136-t-354/t-354-png:file/photo/947119756e749fa5ef5c1a14d6f29dfe63eedd8a/T.354.PNG" alt="" title="T.354.PNG" class="inline" loading="lazy"/></a><br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Csin60%3D%5Cfrac%7B4%7D%7Bx%7D" alt="\sin60=\frac{4}{x}"/></div> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B%5Csqrt%5B%5D%7B3%7D%7D%7B2%7D%3D%5Cfrac%7B4%7D%7Bx%7D" alt="\frac{\sqrt[]{3}}{2}=\frac{4}{x}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%5B%5D%7B3%7Dx%3D8" alt="\sqrt[]{3}x=8"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cfrac%7B8%7D%7B%5Csqrt%7B3%7D%7D" alt="x=\frac{8}{\sqrt{3}}"/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cpi%5Ccdot%5Cleft(%5Cfrac%7B8%7D%7B%5Csqrt%5B%5D%7B3%7D%7D%5Cright)%5E2%3D%5Cpi%5Ccdot%5Cleft(%5Cfrac%7B64%7D%7B3%7D%5Cright)%3D12%5Cpi" alt="\pi\cdot\left(\frac{8}{\sqrt[]{3}}\right)^2=\pi\cdot\left(\frac{64}{3}\right)=12\pi"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=V%3A%5C%20Pinta-ala%5C%20on%5C%2012%5Cpi" alt="V:\ Pinta-ala\ on\ 12\pi"/></div> 2018-02-20T21:50:18+02:00 https://peda.net/id/90f367b8166 2018-02-20T21:05:09+02:00 a)<br/> <a href="https://peda.net/p/kirin_porsti/ma/ma3p/s-134-t-346/t-346-a-png#top" title="T.346 a.PNG"><img src="https://peda.net/p/kirin_porsti/ma/ma3p/s-134-t-346/t-346-a-png:file/photo/9cb7b0cbccc584ceb0fd04342f68170d9f361680/T.346%20a.PNG" alt="" title="T.346 a.PNG" class="inline" loading="lazy"/></a><br/> b) <br/> <a href="https://peda.net/p/kirin_porsti/ma/ma3p/s-134-t-346/t-346-b-png#top" title="T.346 b.PNG"><img src="https://peda.net/p/kirin_porsti/ma/ma3p/s-134-t-346/t-346-b-png:file/photo/18b8da776012733182dc4c5b73378572d2a4f71f/T.346%20b.PNG" alt="" title="T.346 b.PNG" class="inline" loading="lazy"/></a><br/> c)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Calpha%3D60%C2%B0" alt="\alpha=60°"/><br/> <a href="https://peda.net/p/kirin_porsti/ma/ma3p/s-134-t-346/t-346-c-png#top" title="T.346 c.PNG"><img src="https://peda.net/p/kirin_porsti/ma/ma3p/s-134-t-346/t-346-c-png:file/photo/750fffb2d0fe6ab767f34412c6ef825b3303adf7/T.346%20c.PNG" alt="" title="T.346 c.PNG" class="inline" loading="lazy"/></a><br/> <div>d) <br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Csin60%3D%5Cfrac%7Bx%7D%7B4%7D" alt="\sin60=\frac{x}{4}"/></div> <img src="https://math-demo.abitti.fi/math.svg?latex=4%5Ccdot%5Csin60%3Dx" alt="4\cdot\sin60=x"/><br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=x%3D2%5Csqrt%5B%5D%7B3%7D" alt="x=2\sqrt[]{3}"/></div> </div> 2018-02-20T20:55:06+02:00 https://peda.net/id/befc189c166 2018-02-20T20:34:57+02:00 <a href="https://peda.net/p/kirin_porsti/ma/ma3p/s-124-t-334/t-334-png#top" title="T.334.PNG"><img src="https://peda.net/p/kirin_porsti/ma/ma3p/s-124-t-334/t-334-png:file/photo/967f6c492efb5a34f81a54005f0e68b7e027a0e3/T.334.PNG" alt="" title="T.334.PNG" class="inline" loading="lazy"/></a> 2018-02-20T20:34:55+02:00 https://peda.net/id/577ac5d4166 2018-02-20T20:26:33+02:00 <a href="https://peda.net/p/kirin_porsti/ma/ma3p/s-122-t-333/t-333-png#top" title="T.333.PNG"><img src="https://peda.net/p/kirin_porsti/ma/ma3p/s-122-t-333/t-333-png:file/photo/2cef4b87d2ebb24d1d8aa80be87ae66922cdad16/T.333.PNG" alt="" title="T.333.PNG" class="inline" loading="lazy"/></a><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csin30%3D%5Cfrac%7Bx%7D%7Bx%2B6%7D" alt="\sin30=\frac{x}{x+6}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(x%2B6%5Cright)%5Ccdot%5Csin30%3Dx" alt="\left(x+6\right)\cdot\sin30=x"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csin30x%2B%5Csin30%5Ccdot6%3Dx" alt="\sin30x+\sin30\cdot6=x"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csin30x%2B3%3Dx" alt="\sin30x+3=x"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=3%3Dx-x%5Ccdot%5Csin30" alt="3=x-x\cdot\sin30"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=3%3D%5Cleft(1-%5Csin30%5Cright)x" alt="3=\left(1-\sin30\right)x"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cfrac%7B3%7D%7B1-%5Csin30%7D" alt="x=\frac{3}{1-\sin30}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D6" alt="x=6"/> <div> </div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=V%3A%5C%20x%3D6%7B%2C%7D0cm" alt="V:\ x=6{,}0cm"/></div> 2018-02-20T20:24:51+02:00 https://peda.net/id/0e889daa166 2018-02-20T19:55:56+02:00 <a href="https://peda.net/p/kirin_porsti/ma/ma3p/s-122-t-330/t-330-png#top" title="T.330.PNG"><img src="https://peda.net/p/kirin_porsti/ma/ma3p/s-122-t-330/t-330-png:file/photo/39becbdc4f8fa41bc8b26b8c5f9e8b302c141d21/T.330.PNG" alt="" title="T.330.PNG" class="inline" loading="lazy"/></a><br/> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=d%3D36" alt="d=36"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=r%3D%5Cfrac%7B36%7D%7B2%7D%3D18" alt="r=\frac{36}{2}=18"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cbeta%3D2%5Ccdot18%5Cpi%3D36%5Cpi" alt="\beta=2\cdot18\pi=36\pi"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=360%C2%B0%5Ccdot%5Cfrac%7B4%5Cpi%7D%7B36%5Cpi%7D%3D40%C2%B0" alt="360°\cdot\frac{4\pi}{36\pi}=40°"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Calpha%3D%5Cfrac%7B%5Cbeta%7D%7B2%7D%3D%5Cfrac%7B40%C2%B0%7D%7B2%7D%3D20%C2%B0" alt="\alpha=\frac{\beta}{2}=\frac{40°}{2}=20°"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=V%3A%5C%20%5Calpha%3D20%C2%B0" alt="V:\ \alpha=20°"/> 2018-02-20T19:54:11+02:00 https://peda.net/id/17cdcf5a15a 2018-02-19T21:31:10+02:00 a) <br/> Huomasin, kun näitä pisteitä siittretään, vaistaisten kulmien koko pysyvät aina samana.<br/> <a href="https://peda.net/p/kirin_porsti/ma/ma3p/s-122-t-327/t-327-png#top" title="T.327.PNG"><img src="https://peda.net/p/kirin_porsti/ma/ma3p/s-122-t-327/t-327-png:file/photo/e8d8126dd8a0f85df7d3d3a40595cedee45774e5/T.327.PNG" alt="" title="T.327.PNG" class="inline" loading="lazy"/></a><br/> b)<br/> <a href="https://peda.net/p/kirin_porsti/ma/ma3p/s-122-t-327/t-327-b-png#top" title="T.327 b.PNG"><img src="https://peda.net/p/kirin_porsti/ma/ma3p/s-122-t-327/t-327-b-png:file/photo/1e79fb19c4da504ca83bcebec948771e8d0be024/T.327%20b.PNG" alt="" title="T.327 b.PNG" class="inline" loading="lazy"/></a><br/> <br/> <br/> 2018-02-19T21:28:41+02:00 https://peda.net/id/ddcadbba15a 2018-02-20T12:38:38+02:00 <a href="https://peda.net/p/kirin_porsti/ma/ma3p/s-114-t-314/t-314-png2#top" title="T.314.PNG"><img src="https://peda.net/p/kirin_porsti/ma/ma3p/s-114-t-314/t-314-png2:file/photo/2c6bb3142ba1c5f08a9f2f42af51384514cfc77b/T.314.PNG" alt="" title="T.314.PNG" class="inline" loading="lazy"/></a> 2018-02-19T21:48:32+02:00 https://peda.net/id/f77e731015a 2018-02-19T21:43:20+02:00 a)&amp;b)<br/> <a href="https://peda.net/p/kirin_porsti/ma/ma3p/s-114-t-313/t-313-png#top" title="T. 313.PNG"><img src="https://peda.net/p/kirin_porsti/ma/ma3p/s-114-t-313/t-313-png:file/photo/df53a28b536e6727f41762b1cf8ec2198a351f87/T.%20313.PNG" alt="" title="T. 313.PNG" class="inline" loading="lazy"/></a><br/> c) Ymyröiden suhte on 2:1, sillä <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B50%7B%2C%7D27%7D%7B25%7B%2C%7D13%7D%3D2" alt="\frac{50{,}27}{25{,}13}=2"/><br/> <br/> <div> </div> 2018-02-19T21:42:06+02:00 https://peda.net/id/5c0ce966166 2018-02-20T19:46:56+02:00 a) &amp; b)<br/> <a href="https://peda.net/p/kirin_porsti/ma/ma3p/s-112-t-302/t-302-png#top" title="T.302.PNG"><img src="https://peda.net/p/kirin_porsti/ma/ma3p/s-112-t-302/t-302-png:file/photo/b77e79c9a91d6856a8b5f894400fc44bc4e3fc3a/T.302.PNG" alt="" title="T.302.PNG" class="inline" loading="lazy"/></a><br/> c) <br/> Kehän pituus:<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=2%5Ccdot4%5Cpi%3D8%5Cpi" alt="2\cdot4\pi=8\pi"/><br/> Ympyrän pinta-ala:<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=4%5E2%5Cpi%3D16%5Cpi" alt="4^2\pi=16\pi"/><br/> Sektorin pinta-ala:<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=16%5Cpi%5Ccdot%5Cfrac%7B70%7D%7B360%7D%3D%5Cfrac%7B1120%5Cpi%7D%7B360%7D%3D%5Cfrac%7B28%7D%7B9%7D%5Cpi" alt="16\pi\cdot\frac{70}{360}=\frac{1120\pi}{360}=\frac{28}{9}\pi"/><br/> <br/> <br/> 2018-02-20T19:42:02+02:00 https://peda.net/id/939ea87c165 2018-02-20T18:13:27+02:00 <a href="https://peda.net/p/kirin_porsti/ma/ma3p/s-102-t-275/t-275-png#top" title="T.275.PNG"><img src="https://peda.net/p/kirin_porsti/ma/ma3p/s-102-t-275/t-275-png:file/photo/ebd83551c040e78e3d53a862d00ad3996c430c69/T.275.PNG" alt="" title="T.275.PNG" class="inline" loading="lazy"/></a><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=11%3D%5Cfrac%7B1%7D%7B2%7D%5Ccdot8%7B%2C%7D8%5Ccdot5%7B%2C%7D0%5Ccdot%5Csin%5Calpha" alt="11=\frac{1}{2}\cdot8{,}8\cdot5{,}0\cdot\sin\alpha"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=11%3D22%5Ccdot%5Csin%5Calpha" alt="11=22\cdot\sin\alpha"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csin%5Calpha%3D0%7B%2C%7D5" alt="\sin\alpha=0{,}5"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Calpha%3D30" alt="\alpha=30"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%3D8%7B%2C%7D8%5E2%2B5%5E2-2%5Ccdot8%7B%2C%7D8%5Ccdot5%5Ccdot%5Ccos30" alt="x^2=8{,}8^2+5^2-2\cdot8{,}8\cdot5\cdot\cos30"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cpm%5Csqrt%5B%5D%7B8%7B%2C%7D8%5E2%2B5%5E2-2%5Ccdot8.8%5Ccdot5%5Ccdot%5Ccos30%7D" alt="x=\pm\sqrt[]{8{,}8^2+5^2-2\cdot8.8\cdot5\cdot\cos30}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D5%7B%2C%7D121...%5Capprox5%7B%2C%7D1%5Cleft(cm%5Cright)" alt="x=5{,}121...\approx5{,}1\left(cm\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=V%3A%5C%20x%5Capprox5%7B%2C%7D1cm" alt="V:\ x\approx5{,}1cm"/> 2018-02-20T18:10:32+02:00 https://peda.net/id/d89394d6165 2018-02-20T18:14:18+02:00 a)<br/> <a href="https://peda.net/p/kirin_porsti/ma/ma3p/s-111-t-267/t-267-png#top" title="T.267.PNG"><img src="https://peda.net/p/kirin_porsti/ma/ma3p/s-111-t-267/t-267-png:file/photo/096b0f06c3cc63c0f35c4db487d70a4b8ecc8c9f/T.267.PNG" alt="" title="T.267.PNG" class="inline" loading="lazy"/></a><br/> <div> </div> <div><span>b)</span> <div><img src="https://math-demo.abitti.fi/math.svg?latex=9%5E2%3D6%5E2%2B8%5E2-2%5Ccdot6%5Ccdot8%5Ccdot%5Ccos%5Calpha" alt="9^2=6^2+8^2-2\cdot6\cdot8\cdot\cos\alpha"/></div> <img src="https://math-demo.abitti.fi/math.svg?latex=81%3D100-96%5Ccdot%5Ccos%5Calpha" alt="81=100-96\cdot\cos\alpha"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-19%3D-96%5Ccdot%5Ccos%5Calpha" alt="-19=-96\cdot\cos\alpha"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=96%5Ccdot%5Ccos%5Calpha%3D19" alt="96\cdot\cos\alpha=19"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Calpha%3D78%7B%2C%7D584...%5Capprox78%7B%2C%7D58%C2%B0" alt="\alpha=78{,}584...\approx78{,}58°"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B8%7D%7B%5Csin%5Cbeta%7D%3D%5Cfrac%7B9%7D%7B%5Csin%5C%2078%7B%2C%7D58%7D" alt="\frac{8}{\sin\beta}=\frac{9}{\sin\ 78{,}58}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csin%5Cbeta%3D%5Cfrac%7B8%5Ccdot%5Csin78%7B%2C%7D58%7D%7B9%7D" alt="\sin\beta=\frac{8\cdot\sin78{,}58}{9}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csin%5Cbeta%3D0%7B%2C%7D8712..." alt="\sin\beta=0{,}8712..."/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cbeta%3D60%7B%2C%7D598...%5Capprox60%7B%2C%7D60%C2%B0" alt="\beta=60{,}598...\approx60{,}60°"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=180%C2%B0-%5Cleft(78%7B%2C%7D58%C2%B0%2B60%7B%2C%7D60%C2%B0%5Cright)%3D40%7B%2C%7D82%C2%B0" alt="180°-\left(78{,}58°+60{,}60°\right)=40{,}82°"/> <div>78,58 &gt; 60,60 &gt; 40,82<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=V%3A%5C%2078%7B%2C%7D58%C2%B0%5C%20%5Cleft(%E2%88%A2%5Calpha%5Cright)" alt="V:\ 78{,}58°\ \left(∢\alpha\right)"/></div> </div> 2018-02-20T17:50:59+02:00 https://peda.net/id/5c272426165 2018-02-20T17:47:30+02:00 <img src="https://math-demo.abitti.fi/math.svg?latex=AB-CB%5C%20%5Cleft(x%5Cright)" alt="AB-CB\ \left(x\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=CB-DB%5Cleft(y%5Cright)" alt="CB-DB\left(y\right)"/><br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=DB-DE%5Cleft(z%5Cright)" alt="DB-DE\left(z\right)"/></div> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B750%7D%7B%5Csin71%7B%2C%7D5%7D%3D%5Cfrac%7Bx%7D%7B%5Csin57%7B%2C%7D5%7D" alt="\frac{750}{\sin71{,}5}=\frac{x}{\sin57{,}5}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csin71%7B%2C%7D5x%3D379%7B%2C%7D526..." alt="\sin71{,}5x=379{,}526..."/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D667%7B%2C%7D0123..." alt="x=667{,}0123..."/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(CB%5Cright)" alt="\left(CB\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B667%7B%2C%7D0123...%7D%7B%5Csin82%7B%2C%7D6%7D%3D%5Cfrac%7By%7D%7B%5Csin50%7B%2C%7D9%7D" alt="\frac{667{,}0123...}{\sin82{,}6}=\frac{y}{\sin50{,}9}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csin82%7B%2C%7D6y%3D567.632..." alt="\sin82{,}6y=567.632..."/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=y%3D521%7B%2C%7D980..." alt="y=521{,}980..."/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(DB%5Cright)" alt="\left(DB\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B521%7B%2C%7D980...%7D%7B%5Csin32%7D%3D%5Cfrac%7Bz%7D%7B%5Csin35%7B%2C%7D4%7D" alt="\frac{521{,}980...}{\sin32}=\frac{z}{\sin35{,}4}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csin32%3D302%7B%2C%7D373" alt="\sin32=302{,}373"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=z%3D570%7B%2C%7D602...%5Capprox570m" alt="z=570{,}602...\approx570m"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=V%3ADE%5Capprox570m" alt="V:DE\approx570m"/> 2018-02-20T17:47:30+02:00 https://peda.net/id/0e0f6920165 2018-02-20T17:42:46+02:00 <a href="https://peda.net/p/kirin_porsti/ma/ma3p/s-93-t-253/t-253-png2#top" title="T.253.PNG"><img src="https://peda.net/p/kirin_porsti/ma/ma3p/s-93-t-253/t-253-png2:file/photo/529a8be48397557f447e8c29669c982db10a0409/T.253.PNG" alt="" title="T.253.PNG" class="inline" loading="lazy"/></a><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=180%C2%B0-%5Cleft(5%C2%B0%2B90%C2%B0%5Cright)%3D85%C2%B0" alt="180°-\left(5°+90°\right)=85°"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(180%C2%B0-%5Cleft(90%C2%B0%2B7%5Cright)%5Cright)82%7B%2C%7D6%C2%B0" alt="\left(180°-\left(90°+7\right)\right)82{,}6°"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=85%C2%B0-82%7B%2C%7D6%C2%B0%3D2%7B%2C%7D4%C2%B0" alt="85°-82{,}6°=2{,}4°"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=180-%5Cleft(5%C2%B0%2B2%7B%2C%7D4%C2%B0%5Cright)%3D172%7B%2C%7D6%C2%B0" alt="180-\left(5°+2{,}4°\right)=172{,}6°"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B500%7D%7B%5Csin2%7B%2C%7D4%7D%3D%5Cfrac%7By%7D%7B%5Csin172%7B%2C%7D6%7D" alt="\frac{500}{\sin2{,}4}=\frac{y}{\sin172{,}6}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csin2%7B%2C%7D4y%3D64%7B%2C%7D397..." alt="\sin2{,}4y=64{,}397..."/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=y%3D1537%7B%2C%7D833...%5Capprox1538%5Cleft(m%5Cright)" alt="y=1537{,}833...\approx1538\left(m\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B1538%7D%7B%5Csin90%7D%3D%5Cfrac%7Bx%7D%7B%5Csin5%7D" alt="\frac{1538}{\sin90}=\frac{x}{\sin5}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csin90x%3D134%7B%2C%7D045...%5Capprox134%5Cleft(m%5Cright)" alt="\sin90x=134{,}045...\approx134\left(m\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=V%3A%5C%20n.%5C%20134m" alt="V:\ n.\ 134m"/> 2018-02-20T17:38:10+02:00 https://peda.net/id/9c95ceb2165 2018-02-20T17:27:35+02:00 a)<br/> <a href="https://peda.net/p/kirin_porsti/ma/ma3p/s-93-t-252/t-252-png#top" title="T.252.PNG"><img src="https://peda.net/p/kirin_porsti/ma/ma3p/s-93-t-252/t-252-png:file/photo/e00021e853587cfc0f59bc7eae37aa7fbb12c824/T.252.PNG" alt="" title="T.252.PNG" class="inline" loading="lazy"/></a><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=180%C2%B0-%5Cleft(33%C2%B0%2B61%C2%B0%5Cright)%3D86%C2%B0" alt="180°-\left(33°+61°\right)=86°"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B7%7D%7B%5Csin61%7D%3D%5Cfrac%7Bx%7D%7B%5Csin33%7D" alt="\frac{7}{\sin61}=\frac{x}{\sin33}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csin61x%3D3%7B%2C%7D812..." alt="\sin61x=3{,}812..."/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D4%7B%2C%7D359...%5Capprox4%7B%2C%7D4%5Cleft(cm%5Cright)" alt="x=4{,}359...\approx4{,}4\left(cm\right)"/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=BC%5Capprox4%7B%2C%7D4cm" alt="BC\approx4{,}4cm"/><br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B7%7D%7B%5Csin61%7D%3D%5Cfrac%7By%7D%7B%5Csin86%7D" alt="\frac{7}{\sin61}=\frac{y}{\sin86}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csin61y%3D6%7B%2C%7D982..." alt="\sin61y=6{,}982..."/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=y%3D7%7B%2C%7D983...%5Capprox8%7B%2C%7D0%5Cleft(cm%5Cright)" alt="y=7{,}983...\approx8{,}0\left(cm\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=AB%5Capprox8%7B%2C%7D0cm" alt="AB\approx8{,}0cm"/></div> </div> 2018-02-20T17:20:40+02:00 https://peda.net/id/cea25a4e164 2018-02-20T17:07:45+02:00 <span>a)</span> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Ccos%5Calpha%3D%5Cfrac%7B2%7D%7B3%7D" alt="\cos\alpha=\frac{2}{3}"/></div> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Ccos%5Calpha%3D131%7B%2C%7D81...%5Capprox131%7B%2C%7D8%C2%B0" alt="\cos\alpha=131{,}81...\approx131{,}8°"/><br/> <div>b) </div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Csin%5Calpha%3D0%7B%2C%7D25" alt="\sin\alpha=0{,}25"/></div> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csin%5Calpha%3D14%7B%2C%7D477...%5Capprox14%7B%2C%7D5" alt="\sin\alpha=14{,}477...\approx14{,}5"/><br/> <div>c)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Csin%5Calpha%3D1" alt="\sin\alpha=1"/></div> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csin%5Calpha%3D90%C2%B0" alt="\sin\alpha=90°"/> 2018-02-20T17:07:45+02:00 https://peda.net/id/736a0b04164 2018-02-20T17:05:12+02:00 <div>a)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Csin53%3D0%7B%2C%7D798...%5Capprox0%7B%2C%7D8" alt="\sin53=0{,}798...\approx0{,}8"/></div> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7By%7D%7B1%7D%3D%5Cfrac%7B0%7B%2C%7D8%7D%7B1%7D%3D0%7B%2C%7D8" alt="\frac{y}{1}=\frac{0{,}8}{1}=0{,}8"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Ccos53%3D0%7B%2C%7D601...%5Capprox0%7B%2C%7D6" alt="\cos53=0{,}601...\approx0{,}6"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7Bx%7D%7B1%7D%3D%5Cfrac%7B0%7B%2C%7D6%7D%7B1%7D%3D0%7B%2C%7D6" alt="\frac{x}{1}=\frac{0{,}6}{1}=0{,}6"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(0.6%7B%2C%7D0.8%5Cright)" alt="\left(0.6{,}0.8\right)"/><br/> <div>b) </div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=180%C2%B0-143%C2%B0%3D37%C2%B0" alt="180°-143°=37°"/></div> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csin37%3D0%7B%2C%7D601...%5Capprox0%7B%2C%7D6" alt="\sin37=0{,}601...\approx0{,}6"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7By%7D%7B1%7D%3D%5Cfrac%7B0%7B%2C%7D6%7D%7B1%7D%3D0%7B%2C%7D6" alt="\frac{y}{1}=\frac{0{,}6}{1}=0{,}6"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Ccos37%3D0%7B%2C%7D798...%5Capprox0%7B%2C%7D8" alt="\cos37=0{,}798...\approx0{,}8"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7Bx%7D%7B1%7D%3D%5Cfrac%7B-0%7B%2C%7D8%7D%7B1%7D%3D-0%7B%2C%7D8" alt="\frac{x}{1}=\frac{-0{,}8}{1}=-0{,}8"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(-0.8%7B%2C%7D0.6%5Cright)" alt="\left(-0.8{,}0.6\right)"/> 2018-02-20T17:05:11+02:00 https://peda.net/id/dcef5e4a164 2018-02-20T17:01:00+02:00 <div>a)<img src="https://math-demo.abitti.fi/math.svg?latex=Suorakulma" alt="Suorakulma"/></div> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Calpha%3D%5Csin%5Calpha%3D%5Cfrac%7B10%7B%2C%7D4%7D%7B22%7B%2C%7D1%7D" alt="\alpha=\sin\alpha=\frac{10{,}4}{22{,}1}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csin%5Calpha%3D28%7B%2C%7D07...%5Capprox28%7B%2C%7D1" alt="\sin\alpha=28{,}07...\approx28{,}1"/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cbeta%3D%5Csin%5Cbeta%3D%5Cfrac%7B19%7B%2C%7D5%7D%7B22%7B%2C%7D1%7D" alt="\beta=\sin\beta=\frac{19{,}5}{22{,}1}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csin%5Cbeta%3D61%7B%2C%7D92...%5Capprox61%7B%2C%7D9" alt="\sin\beta=61{,}92...\approx61{,}9"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=V%3A%5C%20%5Calpha%5C%20on%5C%20pienempi" alt="V:\ \alpha\ on\ pienempi"/></div> <div>b) </div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=h%3D%5Csin40%3D%5Cfrac%7Bx%7D%7B4%7D" alt="h=\sin40=\frac{x}{4}"/></div> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Csin40%5Ccdot4" alt="x=\sin40\cdot4"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D2%7B%2C%7D571...%5Capprox2%7B%2C%7D57%5Cleft(m%5Cright)" alt="x=2{,}571...\approx2{,}57\left(m\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=A%3D%5Cfrac%7B6%5Ccdot257%7D%7B2%7D%3D7%7B%2C%7D71%5Capprox7%7B%2C%7D7%5Cleft(cm%5E2%5Cright)" alt="A=\frac{6\cdot257}{2}=7{,}71\approx7{,}7\left(cm^2\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=V%3A%5C%20A%5Capprox7%7B%2C%7D7cm%5E2" alt="V:\ A\approx7{,}7cm^2"/> <div> <div> <div> <div> </div> </div> </div> </div> <div> </div> 2018-02-20T17:01:00+02:00 https://peda.net/id/3aa2fdae164 2018-02-20T16:56:30+02:00 <div>a)</div> <img src="https://math-demo.abitti.fi/math.svg?latex=n.7%7B%2C%7D72" alt="n.7{,}72"/> <div>b)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Ccos25%3D%5Cfrac%7B7%7D%7Bx%7D" alt="\cos25=\frac{7}{x}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=7%3D%5Ccos25x" alt="7=\cos25x"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D7%7B%2C%7D7236...%5Capprox7%7B%2C%7D72" alt="x=7{,}7236...\approx7{,}72"/><br/> <a href="https://peda.net/p/kirin_porsti/ma/ma3p/s-72-t-205/t-205-png#top" title="T.205.PNG"><img src="https://peda.net/p/kirin_porsti/ma/ma3p/s-72-t-205/t-205-png:file/photo/5ff13cd9438f50a9ca90f0fdc8b28bce3247dd92/T.205.PNG" alt="" title="T.205.PNG" class="inline" loading="lazy"/></a></div> 2018-02-20T16:56:28+02:00 https://peda.net/id/2595028215a 2018-02-19T21:07:36+02:00 a) Tosi, koska neliöllä on aina samanpituiset sivut ja samankokoiset kulmat.<br/> b) Epätosi, koska eri suorakulmioiden leveys ja korkeus voi olla erilaisessa mittakaavassa.<br/> c) Epätosi, yhdenmuotoisuuteen tarvitaan kaksi samankokoista kulmaa.<br/> d) Tosi, jos korkeus on sama, niiden pinta-alatkin ovat oltava samat. 2018-02-19T21:07:36+02:00 https://peda.net/id/d462329015a 2018-02-19T21:05:20+02:00 a) Ovat, koska iillä on aina samanpituiset sivut ja samankokoiset kulmat, jolloin ne ovat aina yhtenevät.<br/> b) AB:n välissä, koska silloin EF jakaa sunnikan kahden eri sunnikaan, ja lävistäjän avulla sunnikas taas puolintuu, loppuksi jäljellä jäävät kolmiot ovat yhtenevät. 2018-02-19T21:05:20+02:00 https://peda.net/id/81fab1f815a 2018-02-19T21:03:06+02:00 <div>Kolmiot ovat yhdenmuotoiset (kk lause)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B4%7D%7B30%7D%3D%5Cfrac%7Bx%7D%7B7%7B%2C%7D5%7D" alt="\frac{4}{30}=\frac{x}{7{,}5}"/></div> <img src="https://math-demo.abitti.fi/math.svg?latex=30x%3D4%5Ccdot7%7B%2C%7D5" alt="30x=4\cdot7{,}5"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=30x%3D30" alt="30x=30"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D1" alt="x=1"/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=y%3D%5C%202%7B%2C%7D5-1%3D1%7B%2C%7D5%5Cleft(m%5Cright)" alt="y=\ 2{,}5-1=1{,}5\left(m\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=1%7B%2C%7D5%3C1%7B%2C%7D7" alt="1{,}5&lt;1{,}7"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=V%3A%5C%20Kun%5C%20henkil%C3%B6%5C%20on%5C%20pitempi%5C%20kuin%5C%201%7B%2C%7D5cm%5C%20pitk%C3%A4%7B%2C%7D%5C%20se%5C%20n%C3%A4kyy%5C%20ikkunasta" alt="V:\ Kun\ henkilö\ on\ pitempi\ kuin\ 1{,}5cm\ pitkä{,}\ se\ näkyy\ ikkunasta"/><br/> <a href="https://peda.net/p/kirin_porsti/ma/ma3p/s-56-t-176/t-176-png#top" title="T.176.PNG"><img src="https://peda.net/p/kirin_porsti/ma/ma3p/s-56-t-176/t-176-png:file/photo/7a1d4f94b128a00d3c36297db370ed63e1dc1788/T.176.PNG" alt="" title="T.176.PNG" class="inline" loading="lazy"/></a></div> 2018-02-19T21:03:01+02:00 https://peda.net/id/6f0f601215a 2018-02-19T20:55:20+02:00 <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B12%7D%7B5%7D%3D%5Cfrac%7Bx%7D%7B6%7D" alt="\frac{12}{5}=\frac{x}{6}"/></div> <img src="https://math-demo.abitti.fi/math.svg?latex=5x%3D72" alt="5x=72"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D14%7B%2C%7D4" alt="x=14{,}4"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=14%7B%2C%7D4%2B6%3D20%7B%2C%7D4" alt="14{,}4+6=20{,}4"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=V%3A%5C%20BE%3D20%7B%2C%7D4" alt="V:\ BE=20{,}4"/> 2018-02-19T20:55:20+02:00 https://peda.net/id/4adc8aee15a 2018-02-19T20:54:19+02:00 <span>a)</span> <div><img src="https://math-demo.abitti.fi/math.svg?latex=6%5Ccdot%5Cfrac%7B4%7D%7B3%7D%3D8" alt="6\cdot\frac{4}{3}=8"/></div> <img src="https://math-demo.abitti.fi/math.svg?latex=8%5Ccdot%5Cfrac%7B4%7D%7B3%7D%3D10%5Cfrac%7B2%7D%7B3%7D" alt="8\cdot\frac{4}{3}=10\frac{2}{3}"/> <div>b)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B48%7D%7Bx%7D%3D%5Cleft(%5Cfrac%7B4%7D%7B3%7D%5Cright)%5E2" alt="\frac{48}{x}=\left(\frac{4}{3}\right)^2"/></div> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B48%7D%7Bx%7D%3D%5Cfrac%7B10%7D%7B9%7D" alt="\frac{48}{x}=\frac{10}{9}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=16x%3D432" alt="16x=432"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D27" alt="x=27"/><br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B48%7D%7B27%7D%3D%5Cfrac%7B16%7D%7B9%7D%3D16%3A9" alt="\frac{48}{27}=\frac{16}{9}=16:9"/></div> 2018-02-19T20:54:19+02:00 https://peda.net/id/898302d0fa4 2018-01-16T01:34:43+02:00 <a href="https://peda.net/p/kirin_porsti/ma/ma3p/s-42-t-152/t-152-png2#top" title="T.152.PNG"><img src="https://peda.net/p/kirin_porsti/ma/ma3p/s-42-t-152/t-152-png2:file/photo/c2612c9fb23a8eb054742945112501e98dbd3552/T.152.PNG" alt="" title="T.152.PNG" class="inline" loading="lazy"/></a><br/> a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B%5Cfrac%7B5%7D%7B2%7D%5Ccdot%5Cfrac%7B5%7D%7B2%7D%7D%7B2%7D%5Ccdot2%5Ccdot16%3D100" alt="\frac{\frac{5}{2}\cdot\frac{5}{2}}{2}\cdot2\cdot16=100"/><br/> v: Pinta-ala on 100.<br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=Isot%5C%20kolmiot%3A%5C%204%5Ccdot%5Cfrac%7B%5Cfrac%7B5%7D%7B2%7D%5Ccdot%5Cfrac%7B5%7D%7B2%7D%7D%7B2%7D%5Ccdot2%3D25" alt="Isot\ kolmiot:\ 4\cdot\frac{\frac{5}{2}\cdot\frac{5}{2}}{2}\cdot2=25"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=Keski-kokoiset%5C%20kolmiot%3A%5C%2025%3A2%3D12%2C5" alt="Keski-kokoiset\ kolmiot:\ 25:2=12,5"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=Pienet%5C%20kolmiot%3A%5C%2025%3A4%3D6%2C25" alt="Pienet\ kolmiot:\ 25:4=6,25"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=Neli%C3%B6%3A%5C%202%5Ccdot6%2C25%3D12%2C5" alt="Neliö:\ 2\cdot6,25=12,5"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=Sunnikas%3A%5C%202%5Ccdot6%2C25%3D12%2C5" alt="Sunnikas:\ 2\cdot6,25=12,5"/><br/> d)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=Isot%5C%20kolmiot%3A%5C%20hypotennuusa%5C%2010%2C%5C%20kateetut%5C%20x%3D5%5Csqrt%5B%5D%7B2%7D" alt="Isot\ kolmiot:\ hypotennuusa\ 10,\ kateetut\ x=5\sqrt[]{2}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=2x%5E2%3D100%5C%20%5C%20%5C%20%5C%20%5C%20%5Cleft%7C%5Cright%7C%3A2" alt="2x^2=100\ \ \ \ \ \left|\right|:2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%3D50%5C%20%5C%20%5C%20%5C%20%5C%20%5Cleft%7C%5Cright%7C%5Csqrt%5B%5D%7B%7D" alt="x^2=50\ \ \ \ \ \left|\right|\sqrt[]{}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D5%5Csqrt%5B%5D%7B2%7D" alt="x=5\sqrt[]{2}"/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=Keski-kokoiset%5C%20kolmiot%3A%5C%20hypotennuusa%5C%205%5Csqrt%5B%5D%7B2%7D%2C%5C%20kateetit%5C%205" alt="Keski-kokoiset\ kolmiot:\ hypotennuusa\ 5\sqrt[]{2},\ kateetit\ 5"/></div> <img src="https://math-demo.abitti.fi/math.svg?latex=Pienet%5C%20kolmioy%3A%5C%20hypotennuusa%5C%202%2C5%2C%5C%20kateetit%5C%20%5Cfrac%7B5%5Csqrt%5B%5D%7B2%7D%7D%7B2%7D" alt="Pienet\ kolmioy:\ hypotennuusa\ 2,5,\ kateetit\ \frac{5\sqrt[]{2}}{2}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=Neli%C3%B6%3A%5C%20Sivut%5C%20%5Cfrac%7B5%5Csqrt%5B%5D%7B2%7D%7D%7B2%7D" alt="Neliö:\ Sivut\ \frac{5\sqrt[]{2}}{2}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=Sunnikas%3A%5C%20sivut%5C%205%5C%20ja%5C%20%5Cfrac%7B5%5Csqrt%5B%5D%7B2%7D%7D%7B2%7D" alt="Sunnikas:\ sivut\ 5\ ja\ \frac{5\sqrt[]{2}}{2}"/> 2018-01-16T01:26:39+02:00 https://peda.net/id/51864dd2fa4 2018-01-16T00:56:49+02:00 a)<br/> <a href="https://peda.net/p/kirin_porsti/ma/ma3p/s-42-t-148/t-148-a-png#top" title="T.148 a.PNG"><img src="https://peda.net/p/kirin_porsti/ma/ma3p/s-42-t-148/t-148-a-png:file/photo/b60a27f3c924b1ea8e714a11c5b5ae30c8bebf5a/T.148%20a.PNG" alt="" title="T.148 a.PNG" class="inline" loading="lazy"/></a><br/> yksi<br/> <br/> b)<br/> <a href="https://peda.net/p/kirin_porsti/ma/ma3p/s-42-t-148/t-148-b-png#top" title="T.148 b.PNG"><img src="https://peda.net/p/kirin_porsti/ma/ma3p/s-42-t-148/t-148-b-png:file/photo/331e070fad06825fd95c4d72a6a7642616d298d5/T.148%20b.PNG" alt="" title="T.148 b.PNG" class="inline" loading="lazy"/></a><br/> kaksi 2018-01-16T00:56:27+02:00 https://peda.net/id/8e590c2cfa4 2018-01-16T00:22:22+02:00 <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%5B%5D%7B4%5E2-3%5E2%7D%2B%5Csqrt%5B%5D%7B4%5E2-2%5E2%7D%3D6%2C109...%5Capprox6%2C1%5Cleft(m%5Cright)" alt="\sqrt[]{4^2-3^2}+\sqrt[]{4^2-2^2}=6,109...\approx6,1\left(m\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=v%3A%5C%20Noin%5C%206%2C1%5C%20m." alt="v:\ Noin\ 6,1\ m."/> 2018-01-16T00:22:22+02:00 https://peda.net/id/52fe9c1efa4 2018-01-16T00:20:42+02:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=A%3D%5Cfrac%7Bah%7D%7B2%7D%3D%5Cfrac%7B7%5Ccdot2%7D%7B2%7D%3D7%5Cleft(cm%5E2%5Cright)" alt="A=\frac{ah}{2}=\frac{7\cdot2}{2}=7\left(cm^2\right)"/><br/> b) <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=a%5E2%2Bb%5E2%3Dc%5E2" alt="a^2+b^2=c^2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=joten" alt="joten"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=10%5E2%3D6%5E2%2Bx%5E2" alt="10^2=6^2+x^2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%3D10%5E2-6%5E2" alt="x^2=10^2-6^2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%3D64%5C%20%5C%20%5C%20%5C%20%5C%20%5Cleft%7C%5Cright%7C%5Csqrt%5B%5D%7B%7D" alt="x^2=64\ \ \ \ \ \left|\right|\sqrt[]{}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D8%5C%20%5Cleft(cm%5Cright)" alt="x=8\ \left(cm\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=A%3D%5Cfrac%7Bah%7D%7B2%7D%3D%5Cfrac%7B8%5Ccdot6%7D%7B2%7D%3D24%5C%20%5Cleft(cm%5E2%5Cright)" alt="A=\frac{ah}{2}=\frac{8\cdot6}{2}=24\ \left(cm^2\right)"/><br/> c)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=A%3D%5Cfrac%7Bah%7D%7B2%7D%3D%5Cfrac%7B2%5Ccdot5%7D%7B2%7D%3D10%5C%20%5Cleft(cm%5E2%5Cright)" alt="A=\frac{ah}{2}=\frac{2\cdot5}{2}=10\ \left(cm^2\right)"/><br/> d)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=A%3D4%5Ccdot6-%5Cleft(%5Cfrac%7B4%5Ccdot3%7D%7B2%7D%2B%5Cfrac%7B4%5Ccdot6%7D%7B2%7D%5Cright)" alt="A=4\cdot6-\left(\frac{4\cdot3}{2}+\frac{4\cdot6}{2}\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%3D24-%5Cleft(6%2B12%5Cright)" alt="=24-\left(6+12\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%3D6" alt="=6"/> 2018-01-16T00:20:42+02:00 https://peda.net/id/8a48dfe4f56 2018-01-09T20:35:14+02:00 a)<br/> <a href="https://peda.net/p/kirin_porsti/ma/ma3p/s-19-t-110/t-110-png#top" title="T.110.PNG"><img src="https://peda.net/p/kirin_porsti/ma/ma3p/s-19-t-110/t-110-png:file/photo/2052b0a0e717e621fa901b772e217da90db2cc05/T.110.PNG" alt="" title="T.110.PNG" class="inline" loading="lazy"/></a><br/> b)<br/> Kulma b ja c ovat aine yhtä suuret.<br/> c) <br/> Näiden pisteiden välissä muodostuu tasakylkisen kulman, jolla on aina kaksi saman kokoista kulma. 2018-01-09T20:33:08+02:00 https://peda.net/id/ca9d2740f56 2018-02-20T12:47:24+02:00 a)<br/> Suorat a ja b ovat yhdensuuntaiset. Määritä kulmien <span>α ja β suuruudet.</span><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=180%C2%B0-159%C2%B0%3D21%C2%B0" alt="180°-159°=21°"/><br/> Kun suorat a ja b ovat yhdensuuntaiset, kuvasta voidaan päätellä, että kulma <span>α</span> ja β muodostavat ristikulma toistensa kanssa.<br/> Jolloin <span>α</span><span>=</span><span>β<br/> Kulma β' on kulma β:n toinen ristikulma, joka on samana 159° asteen kulman vieruskulma. <br/> <br/> b) <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=134%C2%B0%2B45%C2%B0%3D179%C2%B0%5Cne180%C2%B0" alt="134°+45°=179°\ne180°"/><br/> Ei, koska niiden kahden kulman summa ei ole 180.<br/> <br/> c)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=180%C2%B0-52%C2%B0%3D128%C2%B0" alt="180°-52°=128°"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Calpha%3D128%C2%B0" alt="\alpha=128°"/><br/> <b></b></span> 2018-01-09T20:27:47+02:00