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. (5 points)
554.56 ft
531.86 ft
494.06 ft
509.36ft

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. (5 points)
	554.56 ft
	531.86 ft
	494.06 ft
	509.36ft

anonymous · Answer

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.

anonymous · Answer

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anonymous · Answer

did that help?

naveenbhatia1312 · Answer

I got 549.30 as well but im confused because its not one of the answer choices

anonymous · Answer

what are the answer choices?

naveenbhatia1312 · Answer

554.56 ft
	531.86 ft
	494.06 ft
	509.36ft

anonymous · Answer

oh ummmm let me see with @zepdrix

naveenbhatia1312 · Answer

ok cool

zepdrix · Answer

degrees and minutes? 0_o
ooo this one is annoying.. thinking

zepdrix · Answer

hmm i got one of the answer choices :3
boy this one is tough to explain though...

zepdrix · Answer

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