Question

The angle of depression of a boat from three quarters of a vertical pole is 35º. If the boat is 120 m from the foot of the pole, calculate the height of the pole.​

Answer 1

112 m

Explanation:

The angle of depression from the pole position is the same as the angle of elevation from the boat position. So, the problem statement gives us an angle and horizontal and vertical legs of a right triangle. The relation between them is given by the tangent function.

Tan = Opposite/Adjacent

If we let (3/4h) represent the length of the side opposite the given angle, and 120 m the side adjacent, we have ...

tan(35°) = (3/4h)/(120 m)

Multiplying by the inverse of the coefficient of h, we get ...

h = (160 m)tan(35°) ≈ 112 m

The height of the pole is about 112 meters.