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Thread: IB Math HL Mensuration Question

  1. #1
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    Exclamation IB Math HL Mensuration Question

    The angle of elevation of the top of tower from a point A due south of it is 68 degrees .From a point B due east of A the angle of elevation of the top is 54 degrees. If A is 50 m from B find the height of the tower.
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  2. #2
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    Re: IB Math HL Mensuration Question

    Haven't you tried anything yourself? Start by drawing a picture. There are four triangles involved. Two are the right triangles formed by
    1) the base of the tower, the top of the tower, and point A. It has angle 68 degrees.
    2) the base of the tower, the top of the tower, and point B. It has angle 54 degrees.

    There are two other triangles formed by
    3) the base of the tower, point A, and point B. The side between points A and B is 50 m long.
    4) the top of the tower, point A, and point B.
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  3. #3
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    Re: IB Math HL Mensuration Question

    Let T be the top of the tower, rectangle ABCD where D is the foot of the tower so that
    AB = CD =50 , angle TAD = 68 and angle TBD = 54. Let AD = BC = d and TD = h.

    Let angle TBC = x and angle DBC = y so that x - y = 54

    \tan  x - \tan  y = \frac{h+50}{d}-\frac{50}{d}=\frac{h}{d}=\tan  68

    and

    \tan  x \tan  y = \frac{(h+50)50}{d^2}=\frac{(h+50)50}{h^2/\tan ^2 68}

    Replace these quantities in the identity

    \tan  54 = \tan (x-y)=\frac{\tan  x - \tan  y}{1+\tan  x \tan  y}

    to get a quadratic equation in h

    h=428.49
    Last edited by Idea; Dec 28th 2016 at 12:29 AM.
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  4. #4
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    Re: IB Math HL Mensuration Question

    Hey Gurk99.

    Hint - with mathematical problems it's often a good idea to draw a diagram.
    Thanks from skeeter
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