Question

Two birds sit at the top of two different trees 57.4 feet away from one another. The distance between the second bird and a bird watcher on the ground is 49.6 feet. What is the angle measure, or angle of depression, between the first bird and the bird watcher? © 2011 Jupiter Images Corporation Answer 40.8° 49.2° 30.2° 59.8°

Answer 1

It's 49.1693 which rounds up to 49.2

Answer 2

Answer:

40.8°

Step-by-step explanation:

First, we need to draw the problem. Using each given value, the image attached shows the right triangle formed by these three birds.

It's important to know that the angle of depression is the angle form by the horizontal and the diagonal at the top, like the image shows.

Now, we use trigonometric reasons, specifically, the tangent function which relates both legs.

$tan(x)=\frac{49.6}{57.4} \approx 0.86\\x \approx tan^{-1}(0.86) \\x \approx 40.8\°$

Therefore, the right answer is 40.8°.