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March 25, 2017

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From a weather balloon high in the air, the angle of depression of a ground marker is 27.8 degrees. If the balloon rises 345 m straight up the angle of depression from this higher point is 46.2 degrees. How high above the ground is the balloon?

  • Math 11 - ,

    If the marker is at distance x away from the spot just below the balloon, we have

    h/x = tan 27.8
    (h+345)/x = tan 46.2

    Eliminate x to get

    h/tan 27.8 = (h+345)/tan 46.2
    Now just solve for h.

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