Question

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

Explanation:

Step1: Calculate $\angle X$

The sum of angles in a triangle is $180^\circ$.
$\angle X = 180^\circ - 76^\circ - 36^\circ = 68^\circ$

Step2: Find side $x$ (VW)

Use the Law of Sines: $\frac{x}{\sin\angle X} = \frac{15}{\sin\angle V}$
$x = \frac{15 \times \sin68^\circ}{\sin76^\circ}$
$x \approx \frac{15 \times 0.9272}{0.9703} \approx 14.3$

Step3: Find side $w$ (VX)

Use the Law of Sines: $\frac{w}{\sin\angle W} = \frac{15}{\sin\angle V}$
$w = \frac{15 \times \sin36^\circ}{\sin76^\circ}$
$w \approx \frac{15 \times 0.5878}{0.9703} \approx 9.1$

Answer:

$\angle X = 68^\circ$, $x \approx 14.3$, $w \approx 9.1$