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 17°44'. When the boat stops, the angle of depression is 48°13' . 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.
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Consider the definition of the cotangent function:
.. cot(θ) = A/O
Using that, we can find the required distance as
.. d = (200 ft)*(cot(17°44') -cot(48°13') ≈ 446.71 ft
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