https://peda.net/id/b4b89d661d6 2019-01-21T13:14:23+02:00 https://peda.net/:static/535/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/4d7a80661e1 2019-01-22T08:45:27+02:00 <img src="https://math-demo.abitti.fi/math.svg?latex=%5Ctan54%C2%B0%3D%5Cfrac%7Bx%7D%7B22m%7D" alt="\tan54°=\frac{x}{22m}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D22%5Ctan54%C2%B0" alt="x=22\tan54°"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D30%7B%2C%7D2804...m" alt="x=30{,}2804...m"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Ctan41%C2%B0%3D%5Cfrac%7By%7D%7B22m%7D" alt="\tan41°=\frac{y}{22m}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=y%3D22%5Ctan41%C2%B0" alt="y=22\tan41°"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=y%3D19%7B%2C%7D1243...m" alt="y=19{,}1243...m"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=h%3Dx-y%3D11%7B%2C%7D156...m%5Capprox11m" alt="h=x-y=11{,}156...m\approx11m"/> 2019-01-22T08:45:27+02:00 https://peda.net/id/0246613c1d7 2019-01-21T14:13:49+02:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Calpha%3D%5Cgamma-%5Cbeta" alt="\alpha=\gamma-\beta"/><br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Ctan%5Cbeta%3D%5Cfrac%7B10%7D%7B72%7D%5Cparallel%5Ctan%5E%7B-1%7D" alt="\tan\beta=\frac{10}{72}\parallel\tan^{-1}"/></div> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cbeta%3D7%7B%2C%7D907...%C2%B0" alt="\beta=7{,}907...°"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Ctan%5Cgamma%3D%5Cfrac%7B20%7D%7B72%7D%5Cparallel%5Ctan%5E%7B-1%7D" alt="\tan\gamma=\frac{20}{72}\parallel\tan^{-1}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cgamma%3D15%7B%2C%7D524...%C2%B0" alt="\gamma=15{,}524...°"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Calpha%3D7%7B%2C%7D617...%C2%B0%5Capprox7%7B%2C%7D6%C2%B0" alt="\alpha=7{,}617...°\approx7{,}6°"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Ctan%5Calpha%3D%5Cfrac%7Bx%7D%7B10%7B%2C%7D0%7D" alt="\tan\alpha=\frac{x}{10{,}0}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Ccos25%7B%2C%7D0%C2%B0%3D%5Cfrac%7Bx%7D%7B5%7B%2C%7D2%7D" alt="\cos25{,}0°=\frac{x}{5{,}2}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D5%7B%2C%7D2%5Ccos25%C2%B0" alt="x=5{,}2\cos25°"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D4%7B%2C%7D7128...cm" alt="x=4{,}7128...cm"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Ctan%5Calpha%3D%5Cfrac%7B4%7B%2C%7D712...%7D%7B10%7B%2C%7D0%7D%5Cparallel%5Ctan%5E%7B-1%7D" alt="\tan\alpha=\frac{4{,}712...}{10{,}0}\parallel\tan^{-1}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Calpha%3D25%7B%2C%7D233...%C2%B0%5Capprox25%7B%2C%7D2%C2%B0" alt="\alpha=25{,}233...°\approx25{,}2°"/> 2019-01-21T14:13:49+02:00 https://peda.net/id/4ee20d761e1 2019-01-22T08:38:20+02:00 <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csin25%C2%B0%3D%5Cfrac%7Bx%7D%7B11900m%7D" alt="\sin25°=\frac{x}{11900m}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D11900%5Csin25%C2%B0" alt="x=11900\sin25°"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D5029%7B%2C%7D15...m%5Capprox5029m" alt="x=5029{,}15...m\approx5029m"/> 2019-01-22T08:38:20+02:00 https://peda.net/id/cf7a5a981d7 2019-01-21T14:05:14+02:00 <img src="https://math-demo.abitti.fi/math.svg?latex=A%3Dah" alt="A=ah"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=a%3D320m" alt="a=320m"/><br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Csin40%C2%B0%3D%5Cfrac%7Bh%7D%7B150%7D" alt="\sin40°=\frac{h}{150}"/></div> <img src="https://math-demo.abitti.fi/math.svg?latex=h%3D150%5Csin40%C2%B0" alt="h=150\sin40°"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=h%3D96%7B%2C%7D4181...m" alt="h=96{,}4181...m"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=A%3D320m%5Ccdot96%7B%2C%7D4181...m%3D30853%7B%2C%7D80...m%5E2%5Capprox3%7B%2C%7D1ha" alt="A=320m\cdot96{,}4181...m=30853{,}80...m^2\approx3{,}1ha"/> 2019-01-21T14:05:14+02:00 https://peda.net/id/f301aecc1d7 2019-01-21T13:59:04+02:00 a) tosi<br/> b) epätosi<br/> c) tosi<br/> d) epätosi<br/> e) tosi 2019-01-21T13:59:04+02:00 https://peda.net/id/85b27acc1d7 2019-01-21T13:56:01+02:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csin%5Calpha%3D%5Cfrac%7B28%7D%7B41%7D%5Cparallel%5Csin%5E%7B-1%7D" alt="\sin\alpha=\frac{28}{41}\parallel\sin^{-1}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Calpha%3D43%7B%2C%7D072%C2%B0%5Capprox43%7B%2C%7D1%C2%B0" alt="\alpha=43{,}072°\approx43{,}1°"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Ccos%5Calpha%3D%5Cfrac%7B105%7D%7B135%7D%5Cparallel%5Ccos%5E%7B-1%7D" alt="\cos\alpha=\frac{105}{135}\parallel\cos^{-1}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Calpha%3D38%7B%2C%7D942...%C2%B0%5Capprox38%7B%2C%7D9%C2%B0" alt="\alpha=38{,}942...°\approx38{,}9°"/><br/> <br/> <br/> 2019-01-21T13:56:01+02:00 https://peda.net/id/4c659a7a1d7 2019-01-21T13:47:15+02:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Ctan27%C2%B0%3D%5Cfrac%7Bx%7D%7B8%7B%2C%7D4%7D" alt="\tan27°=\frac{x}{8{,}4}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D8%7B%2C%7D4%5Ctan27%C2%B0" alt="x=8{,}4\tan27°"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D4%7B%2C%7D280...cm%5Capprox4%7B%2C%7D3cm" alt="x=4{,}280...cm\approx4{,}3cm"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Ccos50%C2%B0%3D%5Cfrac%7Bx%7D%7B58%7D" alt="\cos50°=\frac{x}{58}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D58%5Ccos50%C2%B0" alt="x=58\cos50°"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D37%7B%2C%7D2816...cm%5Capprox37cm" alt="x=37{,}2816...cm\approx37cm"/> 2019-01-21T13:47:15+02:00 https://peda.net/id/3ba8a6941d6 2019-01-21T13:25:19+02:00 a) <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Ccos%5Calpha%3D%5Cfrac%7B19%7B%2C%7D5%7D%7B22%7B%2C%7D1%7D%5Cparallel%5Ccos%5E%7B-1%7D" alt="\cos\alpha=\frac{19{,}5}{22{,}1}\parallel\cos^{-1}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Calpha%3D28%7B%2C%7D0724..%C2%B0%5Capprox28%7B%2C%7D1%C2%B0" alt="\alpha=28{,}0724..°\approx28{,}1°"/><br/> b)<br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=A%3D%5Cfrac%7Bah%7D%7B2%7D" alt="A=\frac{ah}{2}"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Ctan40%C2%B0%3D%5Cfrac%7Bh%7D%7B3%7B%2C%7D0%7D" alt="\tan40°=\frac{h}{3{,}0}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=h%3D3%5Ctan40%C2%B0" alt="h=3\tan40°"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=h%3D2%7B%2C%7D5172...cm" alt="h=2{,}5172...cm"/></div> <img src="https://math-demo.abitti.fi/math.svg?latex=A%3D%5Cfrac%7B6%7B%2C%7D0%5Ccdot2%7B%2C%7D5172...%7D%7B2%7D%3D7%7B%2C%7D55189...cm%5E2%5Capprox7%7B%2C%7D6cm%5E2" alt="A=\frac{6{,}0\cdot2{,}5172...}{2}=7{,}55189...cm^2\approx7{,}6cm^2"/> 2019-01-21T13:25:19+02:00 https://peda.net/id/70fd95f81d6 2019-01-21T13:19:39+02:00 a) kolmion saa jaettua kahteen yhtäsuureen suorakulmaiseen kolmioon koska se on tasakylkinen<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Ccos%5Calpha%3D%5Cfrac%7B12%7B%2C%7D0%7D%7B17%7B%2C%7D0%7D%5Cparallel%5Ccos%5E%7B-1%7D" alt="\cos\alpha=\frac{12{,}0}{17{,}0}\parallel\cos^{-1}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Calpha%3D45%7B%2C%7D0991...%C2%B0%5Capprox45%7B%2C%7D1%C2%B0" alt="\alpha=45{,}0991...°\approx45{,}1°"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csin%5Calpha%3D%5Cfrac%7B40%7D%7B45%7D%5Csin%5E%7B-1%7D" alt="\sin\alpha=\frac{40}{45}\sin^{-1}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Calpha%3D62%7B%2C%7D7339...%C2%B0%5Capprox62%7B%2C%7D7%C2%B0" alt="\alpha=62{,}7339...°\approx62{,}7°"/> 2019-01-21T13:19:39+02:00