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Math Help - Angle of elevation problem

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    Angle of elevation problem

    The angle of elevation at the top of a building at point A (on level ground) is 62 degrees. At a point 120m away from A, the angle of elevation is found to be 35 degrees. Find the height of the building.
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    Re: Angle of elevation problem

    Quote Originally Posted by fActor View Post
    The angle of elevation at the top of a building at point A (on level ground) is 62 degrees. At a point 120m away from A, the angle of elevation is found to be 35 degrees. Find the height of the building.
    Have you started by drawing a diagram?
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    Re: Angle of elevation problem

    Quote Originally Posted by Prove It View Post
    Have you started by drawing a diagram?
    Yes, but I'm unsure if the point away from A is supposed to lie on the building. I drew it on the building but didn't get the answer in the textbook (134m)
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    Re: Angle of elevation problem

    Quote Originally Posted by fActor View Post
    Yes, but I'm unsure if the point away from A is supposed to lie on the building. I drew it on the building but didn't get the answer in the textbook (134m)
    I expect that the point away from A is on the ground.
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    Re: Angle of elevation problem

    Quote Originally Posted by Prove It View Post
    I expect that the point away from A is on the ground.
    Oh yeah, you're right. I got the answer now. Thanks!
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    Thumbs up Re: Angle of elevation problem

    Hello, fActor

    From a point A on level ground the angle of elevation to the top of a building is 62o.
    At a point 120m away from A, the angle of elevation is found to be 35o.
    Find the height of the building.

    If you put the point on the building, where is the 35o angle?

    There is basically one diagram that satisfies the description.

    Code:
                                  * T
                              * * |
                          *   *   |
                      *     *     | h
                  *       *       |
              * 35o     * 62o     |
          * - - - - - * - - - - - *
          B    120    A     x     :
    The observer stands at A.
    The angle of elevation to the top of the building (T) is 62o.
    He moves 120 m away from A (and away from the building) to B.
    Now the angle of elevation to T is only 35o.
    We want h, the height of the building.

    Let x be the distance from A to the base of the building.

    We have: . \begin{Bmatrix}\tan62^o &=& \dfrac{h}{x} & [1] \\ \\[-2mm] \tan35^o &=& \dfrac{h}{x+120} & [2] \end{Bmatrix}

    From [1]: . x \:=\:\frac{h}{\tan62^o}\;\;[3]

    From [2]: . x \:=\:\frac{h}{\tan35^o} - 120 \;\;[4]


    Equate [3] and [4] and solve for h.
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