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the angle of elevation from point on the ground to the top of a pyramid is 20 degrees 20 degrees the angle elevation from a point 189 feet farther back to the top of the pyramid is 10 degrees 20 degrees. find the height of the pyramid

  • math -

    tan20o = Y/X1
    Y = X1*tan20.

    tan10o = Y/(X1+X2).
    Y = (X1+X2)*tan10
    X1*tan20 = (X1+X2)*tan10
    X2 = 189 Ft.
    X1*tan20 = (X1+189)*tan10
    X1*tan20 = X1*tan10+189*tan10
    X1*tan20-X1*tan10 = 189*tan10
    0.364X1-0.176X1 = 33.33
    0.188X1 = 33.33
    X1 = 177.3 Ft.

    Y = h = X1*tan20 = 177.3*tan20=64.5 Ft.

  • math -

    NOTE: 2 rt. triangles were formed with a common vert. side and a shared hor. side(X1 and X2).

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