Question

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

Explanation:

Step1: Find angle W via Law of Cosines

Law of Cosines: $\cos(W)=\frac{UW^2 + WV^2 - UV^2}{2 \cdot UW \cdot WV}$
$\cos(W)=\frac{9^2 + 3^2 - 11^2}{2 \cdot 9 \cdot 3}=\frac{81+9-121}{54}=\frac{-31}{54}\approx-0.5741$
$W=\arccos(-0.5741)\approx125.0^\circ$

Step2: Find angle U via Law of Sines

Law of Sines: $\frac{\sin(U)}{WV}=\frac{\sin(W)}{UV}$
$\sin(U)=\frac{WV \cdot \sin(W)}{UV}=\frac{3 \cdot \sin(125.0^\circ)}{11}\approx\frac{3 \cdot 0.8192}{11}\approx0.2234$
$U=\arcsin(0.2234)\approx12.9^\circ$

Step3: Find angle V via angle sum

Triangle angle sum: $U+V+W=180^\circ$
$V=180^\circ - U - W\approx180^\circ - 12.9^\circ - 125.0^\circ=42.1^\circ$

Answer:

$\angle U \approx 12.9^\circ$, $\angle V \approx 42.1^\circ$, $\angle W \approx 125.0^\circ$