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27 December, 03:08

If a plane is cruising at an altitude of 30,0000 feet wants to land at O'Hare, it must begin it's decent so that the angle of depression to the airport is 7 degrees. How many miles from the airport must the plane begin to descend?

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  1. 27 December, 06:02
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    The answer to your question is d = 3683.5 ft

    Step-by-step explanation:

    Data

    Altitude = a = 30, Ф000 ft

    angle = Ф = 7°

    distance = d = ?

    Process

    To solve this problem we must use trigonometric functions. The trigonometric function that relates the Opposite side and the adjacent side is the tangent.

    tan Ф = Opposite site / Adjacent side

    -Solve for Opposite side (d)

    Opposite side = Adjacent side x tan Ф

    - Substitution

    d = 30000 tan 7

    -Simplification

    d = 30000 (0.1228)

    -Result

    d = 3683.5 ft

    -Conclusion

    The plane must begin to descent 3683.5 ft before the airport.
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