Question

solve the right triangle. round your answers to the nearest tenth.

Explanation:

Step1: Find angle B

In a right - triangle, the sum of the two non - right angles is 90°. So $B = 90^{\circ}-39^{\circ}$.
$B = 51^{\circ}$

Step2: Find side b

We know that $\tan39^{\circ}=\frac{b}{24}$. Then $b = 24\times\tan39^{\circ}$.
$b\approx24\times0.8098 = 19.4352\approx19.4$

Step3: Find side c

We know that $\sin39^{\circ}=\frac{24}{c}$. Then $c=\frac{24}{\sin39^{\circ}}$.
$c=\frac{24}{0.6293}\approx38.1$

Answer:

$B = 51^{\circ}$
$b = 19.4$
$c = 38.1$