Math

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A ground observer sights a weather balloon to the east at an angle of elevation of 15º. A second observer 3 miles to the east of the first also sights the balloon to the east at an angle of elevation of 24º. How high is the balloon?

  • Math -

    make a sketch, labeling the balloon P and the point directly below it on the ground as Q
    (We have to find PQ)

    Label the first observer as A and the second as B
    AB = 3
    angle PAB = 15° , angle PBQ = 24°

    In triangle PAB,
    angle A = 15, angle PBA = 156° , so angle APB = 9°

    by the sine law:
    AP/sin15 = 3/sin9
    AP = 3sin15/sin9 = 4.963465... ( I stored in calculator's memory)

    In the right-angled triangle, PBQ
    sin24 = PQ/AP
    PQ = APsin24 = 2.0188 miles high

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