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4 September, 17:18

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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  1. 4 September, 18:13
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    446.71 feet

    Step-by-step explanation:

    17°44' means 17 degrees and 44 minutes. A minute is 1/60 of a degree.

    17°44' = 17 + (44/60) = 17.733°

    Similarly:

    48°13' = 48 + (13/60) = 48.217°

    When the boat is first noticed:

    tan (17.733°) = 200 / a

    a = 200 / tan (17.733°)

    a = 625.43

    When the boat stops:

    tan (48.217°) = 200 / b

    b = 200 / tan (48.217°)

    b = 178.72

    So the difference is:

    a - b = 625.43 - 178.72 = 446.71

    The boat traveled 446.71 feet from the time it was first noticed to the time it stopped.
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