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two points A and B 80 ft. apart lie on the same side of a tower and in a horizontal line through its foot. if the angle of elevation of the top of the tower at A is 21 degree and B is 46 degree, find the height of the tower.

  • math -

    Let P be the foot of the tower, and h be the height of the tower
    let AP = x , then BP = 80-x
    I see two right-angled triangles

    tan21 = h/x ---> h = xtan21
    tan46 = h/(80-x) --> h = (80-x)tan46

    xtan21 = (80-x)tan46
    xtan21 = 80tan46 - xtan46
    xtan21 + xtan46 = 80tan46
    x(tan21 + tan46) = 80tan46
    x = 80tan46/(tan21 + tan46) ----- I have not yet touched a calculator

    you do the button pushing to get x
    then plug x into
    h = xtan21

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