2.4

270

a) kosinilause
$c^2=a^2+b^2-2ab\cos\gamma$

$c=\pm4.55244...$

hylätään negatiivinen tulos

$c=4{,}55244...\approx4{,}6cm$

b) sinilause

$\frac{a}{\sin\alpha}=\frac{b}{\sin\beta}=\frac{c}{\sin\gamma}$

kolmas kulma on $180°-60°-70°=50°$
$\frac{3{,}0cm}{\sin50°}=\frac{x}{\sin60°}$
$3\sin60°=x\sin50°$
$2{,}598...cm=x\sin50°\ \parallel:\sin50°$
$x=3{,}391...cm\approx3{,}4cm$

c) kosinilause
$c^2=a^2+b^2-2ab\cos\gamma$
$3{,}5^2=3{,}5^2+6{,}4^2-2\cdot3{,}5\cdot6{,}4\cos\gamma$
$12{,}25=53.21-44.8\cos\gamma\$
$44.8\cos\gamma=40.96\ \parallel:44.8$
$\cos\gamma=\frac{40.96}{44.8}$
$\gamma=23{,}89550...°\approx23{,}9°$

278

$c^2=a^2+b^2-2ab\cos\gamma$
$5{,}8^2=4{,}8^2+x^2-2\cdot4{,}8\cdot x\cdot\cos\ 40°$
$ratkaistaan\ x\ laskimella$
$x\approx8{,}59\ tai\ x\approx-1{,}23\ \left(hylätään\right)$
$x\approx8{,}6cm$

275

$A=\frac{1}{2}ab\sin\gamma$
$11=\frac{1}{2}\cdot5\cdot8{,}8\sin\gamma$
$11=22\sin\gamma\ \parallel:22$
$0{,}5=\sin\gamma\$
$\gamma=30°\ tai\ 180°-30°=150°$
$c^2=a^2+b^2-2ab\cos\gamma$
$c^2=26.229...cm\ tai\ 178.650...cm\ \parallel\sqrt{ }$

$c=\pm5{,}121...\ \approx\pm5{,}1cm\ tai\ \pm13.366...\approx\pm13{,}4cm$

hylätään negatiiviset tulokset

$c=5{,}1cm\ tai\ 13{,}4cm$