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\$
$44.8\cos\gamma=40.96\ \parallel:44.8$
$\cos\gamma=\frac{40.96}{44.8}$
$\gamma=23{,}89550...°\approx23{,}9°$