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I'm not sure how to work this problem out. Find it very confusing and my answer keeps changing. Please help.

From an observation tower that overlooks a runway, the angles of depression of point A, on one side of the runway, and point B, on the opposite side of the runway are 6 degrees and 13 degrees, respectively. The points and the tower are in the same vertical plane and the distance from A to B is 1.1 km. Determine the height of the tower.

  • math - ,

    make a diagram, label the base of the tower T, and let the height of the tower be h
    let AT=x, then TB = 1.1-x
    in 1st triangle:
    tan6 = h/x ---> h = xtan6
    in 2nd triangle:
    tan 13 = h/(1.1-x) --> h = (1.1-x)tan13

    then xtan6 = 1.1tan13 - xtan13
    xtan6 + xtan13 = 1.1tan13
    x(tan6 - tan13) = 1.1tan13
    x = 1.1tan13/(tan6 + tan13)

    once you found x, sub that into h = xtan6
    to get the height.

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