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 your answer to the hundredths place.

509.35 feet

Step-by-step explanation:

16°23' means 16 degrees and 23 minutes. A minute is 1/60 of a degree.

16°23' = 16 + (23/60) = 16.383°

Similarly:

49°29' = 49 + (29/60) = 49.483°

When the boat is first noticed:

tan (16.383°) = 200 / a

a = 200 / tan (16.383°)

a = 680.27

When the boat stops:

tan (49.483°) = 200 / b

b = 200 / tan (49.483°)

b = 170.92

So the difference is:

a - b = 680.27 - 170.92 = 509.35

The boat traveled 509.35 feet from the time it was first noticed to the time it stopped.