Question

Math question.... almost finished but uncertain on one part
Ted 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.

I think I have some of it down...
200/tan(16.18)

200/tan(48.51)

then subtract the solutions... is this the right path or no?

Answer 1

i think this might be it if so let me know

Page 1
Answer on Question #42535, Math, Calculus
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°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.
Calculate initial distance between boat and lighthouse.
We know one cathetus and angle of desperssion.
200 ∗ (90° − 16°18′) = 683.95
Calculate distance between boat and lighthouse when it stopped.
200 ∗ (90° − 48°51) = 174.78
Find difference:
Length = 683.95 – 174.78 = 509.17
Answer: 509.17 meters

Answer 2

That question seems very similar. Im not sure if you can help but do you know why 90 degrees?

Answer 3

i am not quite sure, i am sorry but i do not know

Answer 4

Thats okay... I'll leave it open and see if anyone else can answer that