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25 June, 07:00

A balloon flying at 3000 feet above the ocean measures the angles of depression of each end of an island directly in front of the balloon to be 75.8° and 15.6°. What is the length of the island to the nearest tenth of a mile?

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  1. 25 June, 07:23
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    The length of the island will be given as follows:

    tan θ=opposite/adjacent

    thus:

    tan75.8 = 3000/a1

    a1=3000tan75.8

    a1=11855.885 ft

    also:

    tan15.6=3000/a2

    a2=3000tan15.6

    a2=837.62 ft

    Thus the length of the island will be:

    11855.885-837.615

    =11,018.24 ft
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