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 = 56°34', convert 34' to degrees: 34' = $\frac{34}{60}\approx0.57$°, so A = 56.57°. Then B = 90° - 56.57° = 33.43°≈33°26'.

Step2: Find side a

We know that $\sin A=\frac{a}{c}$, where c = 962 m. So a = c×$\sin A$. $\sin(56.57^{\circ})\approx0.834$, then a = 962×0.834 = 802.308≈802 m.

Step3: Find side b

We know that $\cos A=\frac{b}{c}$, where c = 962 m. So b = c×$\cos A$. $\cos(56.57^{\circ})\approx0.551$, then b = 962×0.551 = 530.062≈530 m.

Answer:

B = 33°26'
a = 802 m
b = 530 m