Question

solve the right triangle. round your answers to the nearest tenth. b = 31°, b = 41.6, c = 48.5

Explanation:

Step1: Find angle A

In a right - triangle, the sum of the interior angles is 180°. Since one angle is 90° and B = 31°, then A=180° - 90° - 31° = 59°.

Step2: Use tangent to find side a

We know that $\tan B=\frac{b}{a}$. Given B = 31° and b = 41.6, then $a=\frac{b}{\tan B}=\frac{41.6}{\tan31^{\circ}}$. Since $\tan31^{\circ}\approx0.6009$, $a=\frac{41.6}{0.6009}\approx69.2$.

Step3: Use sine to find side c

We know that $\sin B=\frac{b}{c}$. Given B = 31° and b = 41.6, then $c=\frac{b}{\sin B}=\frac{41.6}{\sin31^{\circ}}$. Since $\sin31^{\circ}\approx0.5150$, $c=\frac{41.6}{0.5150}\approx80.8$.

Answer:

A = 59°, a≈69.2, c≈80.8