Question

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

Explanation:

Step1: Find angle at W

The sum of angles in a triangle is $180^\circ$.
$\angle W = 180^\circ - 13^\circ - 143^\circ = 24^\circ$

Step2: Solve for side $x$ (VW)

Use the Law of Sines: $\frac{x}{\sin X} = \frac{XV}{\sin W}$
$\frac{x}{\sin 13^\circ} = \frac{9}{\sin 24^\circ}$
$x = \frac{9 \times \sin 13^\circ}{\sin 24^\circ}$
Calculate $\sin 13^\circ \approx 0.2250$, $\sin 24^\circ \approx 0.4067$
$x \approx \frac{9 \times 0.2250}{0.4067} \approx 4.9$

Step3: Solve for side $v$ (XW)

Use the Law of Sines: $\frac{v}{\sin V} = \frac{XV}{\sin W}$
$\frac{v}{\sin 143^\circ} = \frac{9}{\sin 24^\circ}$
$\sin 143^\circ = \sin(180^\circ-37^\circ) = \sin 37^\circ \approx 0.6018$
$v = \frac{9 \times \sin 143^\circ}{\sin 24^\circ} \approx \frac{9 \times 0.6018}{0.4067} \approx 13.3$

Answer:

$\angle W = 24^\circ$, $x \approx 4.9$, $v \approx 13.3$