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4 October, 11:18

To approach the runway, a pilot of a small plane must begin a 5 degree descent starting from a height of 1407 feet above the ground. To the nearest tenth of a mile, how many miles from the runway is the airplane at the start of this approach?

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  1. 4 October, 13:10
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    3.0 miles

    Step-by-step explanation:

    The tangent of the angle relates the opposite side (altitude) to the adjacent side (distance to runway):

    tan (5°) = (altitude) / (distance to runway)

    Then we have ...

    distance to runway = (1407 ft) / (tan 5°) ≈ 16,082 ft

    In miles, that is ...

    distance to runway = (16082 ft) / (5280 ft/mi) = 3.0458 mi

    The pilot is 3.0 miles from the runway at the start of his approach.
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