trigonometry

Solution of problem:from the top of a building 55 ft high, the angle of elevation of the top of a vertical pole is 12 degrees, At the bottom of the building, the angle of elevation of the top of the pole is 24 degrees. find the height of the pole.

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  1. Hoping you made a diagram,
    label the top of the pole P and its bottom Q
    label the top of the building A and its bottom B

    Now look at triangle PAB.
    angle PAB = 90+12 = 102°
    angle PBA = 90-24 = 66°
    leaving angle APB = 12°

    by the sine law:
    PB/sin102 = 55/sin12
    PB = 55sin102/sin12 , don't work it out yet

    in right-angled triangle PQB
    sin 24 = PQ/PB
    PQ = PB sin24 = 55 sin102 sin24/sin12

    now get your calculator out, and do it in one continuous operation.

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  2. 105.25ft

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