Question

A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed the angle of depression to the boat is 16° 23'. When the boat stops, the angle of depression is 49° 29'. The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round to the nearest hundredth.

Answer 1

This is not difficult. Use the tangent function of each angle.

tan Θ = height of lighthouse / distance of boat from lighthouse.

tan (15.85°) = 200 / x
x = 200 / tan 15.85°
x ≈ 704.438 ft

tan (52.2°) = 200 / x'
x' = 200 / tan (52.2°)
x' ≈ 155.136 ft..

The distance the boat traveled is equal to x - x':

x - x' = 704.438 ft - 155.136 ft = 549.302 ft.

We can then round the answer to 549.30 ft.

Answer 2

got it thanksssss :)