Question

two birds sit at the top of two different trees. the distance between the first bird and a birdwatcher on the ground is 34 feet. the distance between the birdwatcher and the second bird is 47 feet.
what is the angle measure, or angle of depression, between this bird and the birdwatcher? round your answer to the nearest tenth.
43.7°
35.9°
54.1°
46.3°

Explanation:

Step1: Use trigonometric ratio

In a right - triangle, we know that \(\tan x=\frac{\text{opposite}}{\text{adjacent}}\). Here, the opposite side to angle \(x\) is \(34\) (distance between first bird and birdwatcher) and the adjacent side is \(47\) (distance between the two birds). So, \(\tan x=\frac{34}{47}\).

Step2: Calculate the angle

We have \(x = \arctan(\frac{34}{47})\). Using a calculator, \(x=\arctan(0.7234)\approx35.9^{\circ}\)

Answer:

\(35.9^{\circ}\)