Aperson 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°18'. when the boat stops, the angle of depression is 48°51'. 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.

To solve this problem, we can use the tan function to find for the distances covered.

tan θ = o / a

Where,

θ = angle = 90° - angle of depression

o = side opposite to the angle = distance of boat from lighthouse

a = side adjacent to the angle = height of lighthouse = 200 ft

When the angle of depression is 16°18', the initial distance from the lighthouse is:

o = 200 tan (90° - 16°18')

o = 683.95 ft

When the angle of depression is 48°51', the final distance from the lighthouse is:

o = 200 tan (90° - 48°51')

o = 174.78 ft

Therefore the total distance the boat travelled is:

d = 683.95 ft - 174.78 ft

d = 509.17 ft

answer: can and shows the work

step-by-step explanation: