Question

solve the right triangle. b = (round to the nearest integer as needed.) a = m (round to the nearest integer as needed.) b = m (round to the nearest integer as needed.)

Explanation:

Step1: Find angle B

In a right - triangle, the sum of the two non - right angles is 90°. Given angle A = 50°28', convert 28' to degrees: 28'=$\frac{28}{60}\approx0.47$°, so A = 50.47°. Then B = 90° - 50.47° = 39.53°≈39°32'.

Step2: Find side a

We know that $\sin A=\frac{a}{c}$, where c = 963 m. So a = c×$\sin A$. $\sin(50.47^{\circ})\approx0.77$, then a = 963×0.77≈741 m.

Step3: Find side b

We know that $\cos A=\frac{b}{c}$, so b = c×$\cos A$. $\cos(50.47^{\circ})\approx0.64$, then b = 963×0.64≈616 m.

Answer:

B = 39°32'
a = 741 m
b = 616 m