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12 December, 00:01

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.

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  1. 12 December, 00:12
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    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.
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