Question

A lighthouse keeper views a small boat at an angle of depression of 62 degrees. The boat is 446 feet away from the base of the lighthouse. How tall is the lighthouse?

Answer 1

Answer: the height of the lighthouse is 838.8 feet

Step-by-step explanation:

The right angle triangle ABC illustrating the scenario is shown in the attached photo.

The angle of depression and angle A are alternate angles, hence, they are the equal.

The height, h of the lighthouse represents the opposite side of the right angle triangle. The distance of the boat from the foot of the lighthouse represents the adjacent side of the right angle triangle.

To determine h, we would apply

the tangent trigonometric ratio.

Tan θ, = opposite side/adjacent side. Therefore,

Tan 62 = h/446

h = 446tan62 = 446 × 1.8807

h = 838.8 feet to the nearest tenth.