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The angle of elevation from a point on the ground to the top of a tree is 38 degrees. The angle of elevation from a point 22.5 ft farther back to the top of the tree is 28.2 degrees. Find the height of the tree to 2 decimal places.

could you help me out..I got this so far..thanks

h/(tan38(=h/(tan28.2)-29

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1 answer

  1. Make a sketch.
    On the ground line, mark off the bottom of the tree as Q, your first position
    as A and your second point further back as B.
    Label the top of the tree as P

    So we want to find PQ

    In triangle PBA, we know angle PBA = 28.2° and angle PAQ = 142°,
    which make angle APB = 9.8°

    by the sine law:
    22.5/sin9.8 = AP/sin28.2°
    AP = 22.5 sin28.2/sin 9.8 = 62.4665... ( I stored that in memory)

    In the right-triangle APQ
    sin 38 = PQ/AP
    PQ = APsin38 = 62.4665..(sin38) = 38.458..
    = 38.46 ft

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