Question

solve the triangle.
write each answer as an integer or as a decimal rounded to the nearest tenth.

Explanation:

Step1: Find angle V via Law of Cosines

$\cos(V)=\frac{5^2+11^2-15^2}{2(5)(11)}$
$\cos(V)=\frac{25+121-225}{110}=\frac{-79}{110}\approx-0.7182$
$\angle V=\arccos(-0.7182)\approx135.9^\circ$

Step2: Find angle U via Law of Sines

$\frac{\sin(U)}{11}=\frac{\sin(135.9^\circ)}{15}$
$\sin(U)=\frac{11\sin(135.9^\circ)}{15}\approx\frac{11\times0.695}{15}\approx0.5123$
$\angle U=\arcsin(0.5123)\approx30.8^\circ$

Step3: Find angle W via angle sum

$\angle W=180^\circ-135.9^\circ-30.8^\circ$
$\angle W\approx13.3^\circ$

Answer:

$\angle U \approx 30.8^\circ$, $\angle V \approx 135.9^\circ$, $\angle W \approx 13.3^\circ$