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Math Help - trigonometry

  1. #1
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    trigonometry

    A vertical tower stands on horizontal ground . The angle of elevation on the top T , of the tower from a point P south of the tower is 50 degree and the angle of elevation of T from a point Q west of the tower is 32 degree . Given that the distance PQ is 150 m , calculate the height of the tower .

    When the question says south , does it mean exactly south of the tower ? If so , how can it be 50 degree , should be 90 degrees ??
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  2. #2
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    Quote Originally Posted by thereddevils View Post
    A vertical tower stands on horizontal ground . The angle of elevation on the top T , of the tower from a point P south of the tower is 50 degree and the angle of elevation of T from a point Q west of the tower is 32 degree . Given that the distance PQ is 150 m , calculate the height of the tower .

    When the question says south , does it mean exactly south of the tower ? Yes If so , how can it be 50 degree , should be 90 degrees ??
    1. Draw a sketch (see attachment)

    2. The foot of the tower, P and Q are the vertices of a right triangle because the directions West and South include 90.

    3. Let x, y denote the legs of this right triangle and h the height of the tower. Then you'll get:

    x = \dfrac h{\tan(32^\circ)}

    y = \dfrac h{\tan(50^\circ)}

    4. Now use Pythagorean theorem:

    x^2 + y^2 = 150^2 Substitute x and y and solve this equation for h.
    Attached Thumbnails Attached Thumbnails trigonometry-turmhoehe.png  
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  3. #3
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    REally thank you earboth , appreciate that .. Btw what software did u use to draw such diagrams , looks so useful . I bet many hv asked this ..
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  4. #4
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    Quote Originally Posted by thereddevils View Post
    REally thank you earboth , appreciate that .. Btw what software did u use to draw such diagrams , looks so useful . I bet many hv asked this ..
    Thanks for your interest but...


    I need a sketch myself to understand the question.
    I convert my drawing (done by hand) into a graphic using MS Paint.

    So nothing miraculous or expensive - only a program from the stone age of computer science.
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