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Math Help - Height of chimney stack using Angles of Elevation

  1. #1
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    Height of chimney stack using Angles of Elevation

    Hello, can anyone help me out with this:


    At a point А due south of a chimney staсk, the angle of elevation
    of the staсk is 55 degrees. From B, due west of А, such that АB = 100
    m, the elevation of the staсk is 33 degrees. Find the height of the stake
    and its horizontal distance from А.
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  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    You have to draw a diagram to see what is happening.

    Stack.pdf

    Sorry I still can't upload images but here is a PDF with the pictures.

    From this we can use the Pythagorean theorem to get

    d_1^2+100^2=d_2^2

    Now using the angles of elevation we get

    \tan(55^{\circ})=\frac{h}{d_1} \iff d_1=\frac{h}{\tan(55^\circ)}

    \tan(33^{\circ})=\frac{h}{d_2} \iff d_2=\frac{h}{\tan(33^\circ)}

    Now just plug d_1,d_2 into the first equation and solve for h.
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  3. #3
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    Oh now i get it... Thanks a lot!
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