A bird (B) is spotted flying 5,000 feet from a tree (T). An observer (O) spots the bird (B) at a distance of 13,000 feet. What is the angle of depression from the bird (B) to the observer (O)?

Right triangle OTB is shown. Side TB is labeled 5,000 and side BO is labeled 13,000. The angle B is labeled x degrees.

22.70°
44.62°
67.38°
68.96°

Answers

Answer 1

The angle of depression from the bird (B) to the observer (O) is approximately 22.70°.

How to solve for the angle of depression

To find the angle of depression from the bird (B) to the observer (O), we can use the tangent function, which relates the angle to the lengths of the sides of the right triangle.

In this case, we have side TB (opposite) with a length of 5,000 feet and side BO (adjacent) with a length of 13,000 feet. We want to find the angle B (x degrees).

The tangent of angle B is given by:

tan(B) = Opposite/Adjacent = TB/BO

Substituting the values:

tan(B) = 5,000/13,000

Using a calculator, we can find the value of B by taking the inverse tangent (arctan) of both sides:

B = arctan(5,000/13,000)

The approximate value of B, to two decimal places, is 22.70°.

Therefore, the angle of depression from the bird (B) to the observer (O) is approximately 22.70°.

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