Question

A bird (B) is spotted flying 900 feet from an observer. The observer (O) also spots the top of a tower (T) at a height of 200 feet. What is the angle of depression from the bird (B) to the observer (O)?

Right triangle OTB is shown. Side OT is labeled 200 and side BO is labeled 900. The angle B is labeled x degrees.

12.52°
12.84°
77.16°
83.69°

Answer 1

it is 12.84 =)

Answer 2

X = 12.84°

Explanation:

Here, we want to find the measure of the angle labeled x

To do this, we use the appropriate trigonometric identity

From the diagram, we have it that the side 200 which the angle x faces is the opposite, the other side of 900 is the hypotenuse which is the longest side and the side that faces the right angle

The trigonometric identity that relates opposite to the hypotenuse is the sine

Thus;

sin x = 200/900

sin x = 2/9

sin x = 0.222

x = arc•sin (0.222)

x = 12.84 degrees