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  1. #1
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    Question bearings.. help

    Height of a tower
    From a point P on level ground, the angle of elevation of the top of a tower is 26 50.' From a point 25meters closer to the tower and on the same line with P and the base of the tower, the angle of elevation of the top is 5330.' Approximate the height of the tower.



    _______________________
    25m


    tan 2650'=height (OPPOSITE)
    25m+x


    tan53 30'=h
    x


    Generalize to the case where the first angle is alpha, the second angle is beta, and the distance between the two points is d. Express the height h of the tower in terms of d, alpha and beta.


    ά=tan inverse htx
    25 meters

    β=90-ά
    Last edited by cocoknny; October 16th 2007 at 02:38 PM.
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  2. #2
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    Quote Originally Posted by cocoknny View Post
    Generalize to the case where the first angle is alpha, the second angle is beta, and the distance between the two points is d. Express the height h of the tower in terms of d, alpha and beta.


    ά=tan inverse htx
    25 meters

    β=90-ά
    Let the distance between point P and the tower be x. Let the height of the tower be y.

    Then
    tan(\alpha) = \frac{y}{x}
    and
    tan(\beta) = \frac{y}{x - d}

    We need to solve for y, given \alpha, \beta, and d.

    So from the first equation:
    x = \frac{y}{tan(\alpha)}

    Inserting this value of x into the second equation gives:
    tan(\beta) = \frac{y}{\frac{y}{tan(\alpha)} - d}

    tan(\beta) = \frac{y}{\frac{y}{tan(\alpha)} - d} \cdot \frac{tan(\alpha)}{tan(\alpha)}

    tan(\beta) = \frac{y~tan(\alpha)}{y - d~tan(\alpha)}

    Can you finish it from here?

    -Dan
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by cocoknny View Post
    y___
    y-d
    What is this?

    Quote Originally Posted by cocoknny View Post
    is my top part right?
    I don't know because I don't know what "htx" is supposed to mean.

    -Dan
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    tan 2650'=h
    25m+x
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  5. #5
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    hello

    Oh don't worry about that part. h suppose to be the height
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by cocoknny View Post
    tan 2650'=h
    25m+x
    It looks good if you have defined x as the distance from the second point to the tower.

    That's one equation. You need to use the other to eliminate x.

    -Dan
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  7. #7
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    hello

    YUP that's what i did. Thanks hun
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