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, $B=90^{\circ}-59^{\circ}$.
$B = 31^{\circ}$

Step2: Find side b

We know that $\tan A=\frac{a}{b}$. Here, $A = 59^{\circ}$ and the adjacent side to $A$ is 25. So, $\tan59^{\circ}=\frac{b}{25}$, then $b = 25\times\tan59^{\circ}$.
$b=25\times1.664279\approx41.6$

Step3: Find side c

We know that $\cos A=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $A = 59^{\circ}$ and the adjacent side to $A$ is 25. So, $\cos59^{\circ}=\frac{25}{c}$, then $c=\frac{25}{\cos59^{\circ}}$.
$c=\frac{25}{0.515038}\approx48.5$

Answer:

$B = 31^{\circ}$
$b\approx41.6$
$c\approx48.5$