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°. $B = 90^{\circ}-50^{\circ}=40^{\circ}$

Step2: Find side a

We know that $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\tan(50^{\circ})=\frac{a}{24}$, so $a = 24\times\tan(50^{\circ})\approx24\times1.192 = 28.6$

Step3: Find side c

We know that $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\cos(50^{\circ})=\frac{24}{c}$, so $c=\frac{24}{\cos(50^{\circ})}\approx\frac{24}{0.643}\approx37.3$

Answer:

$B = 40^{\circ}$ $a = 28.6$ $c = 37.3$