Question

solutions and applications of right
question 1, 5.4.15
hw score: 0%, 0 of 100 points
points: 0 of 7
solve the right triangle
b = 33° 26 (round to the nearest integer as needed.)
a =
(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'. First convert 56°34' to decimal degrees. 34' = $\frac{34}{60}\approx0.57$°, so A = 56.57°. Then B = 90° - 56.57° = 33.43°. Converting back to degrees and minutes, 0.43°×60 = 25.8'≈26', so B = 33°26'.

Step2: Find side a

We know that $\sin A=\frac{a}{c}$, where c = 982 m. So a = c×$\sin A$. $\sin(56.57°)\approx0.834$, then a = 982×0.834 = 820.988≈821 m.

Step3: Find side b

We know that $\cos A=\frac{b}{c}$, where c = 982 m. So b = c×$\cos A$. $\cos(56.57°)\approx0.551$, then b = 982×0.551 = 541.082≈541 m.

Answer:

a = 821 m
b = 541 m