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 13°32'. When the boat stops, the angle of depression is 45°10'. The lighthouse is 160 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place.

Answer 1

Draw a diagram. You will see that if the distance moved is x, then
x = 160cot13°32' - 160cot45°10'