Question

13. You are at the top of a lighthouse that is 400 ft. Tall. You look down towards the ocean and see a whale located 700 ft. From the shore. What is the angle of depression from your position?

Answer 1

29.7°

Explanation:

In a right triangle representing the geometry of the problem, the side opposite the angle is the height of your observation (400 ft). The side adjacent to the angle is the distance from shore (700 ft).

You know the tangent ratio is ...

Tan = Opposite/Adjacent

so your angle of depression satisfies ...

tan(angle of depression) = (400 ft)/(700 ft)

Using the inverse function, we find ...

angle of depression = arctan(4/7) ≈ 29.745°

The angle of depression is about 29.7°.