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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.

Please verify if 72.2 meters is the height of the tower.

  • math -

    Label the figure, T is the top of the tower, Dis the base of the tower.

    angle DAT=13
    angle DB=6
    AB = 1100m

    find DT

    from the figure, AT/sin13=1100/Sin(13-6) solve for AT.
    then, AT/sin90=DT/sin13

  • math -

    Thanks for your help, I guess we took different approaches to this so now I'm a little confused. Is it possible to explain a little clearer?

  • math -

    I drew the figure. I saw two triangles. In one, I used the law of sines (I knew two angles, one side) to find the other side, then used that side (common to the other triangle, to solve height with the law of sines again.

  • math -

    Wonderful help. Thank you.

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