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Math Help - engineering word

  1. #1
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    Wink engineering word

    The surface of a section of highway makes an angle of A degees with the horizontal. An engineer has found that for a particular section, (d^2-d^2cos^2A)/(d^2-d^2sin^2A) =9/400, where d is the distance along the surface of the road.

    a. Make a labeled drawing of the situation.

    b. Find a numerical value for one trigonometric function of A.
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  2. #2
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    Quote Originally Posted by mathAna1ys!5
    The surface of a section of highway makes an angle of A degees with the horizontal. An engineer has found that for a particular section, (d^2-d^2cos^2A)/(d^2-d^2sin^2A) =9/400, where d is the distance along the surface of the road.

    a. Make a labeled drawing of the situation.

    b. Find a numerical value for one trigonometric function of A.
    a)I have no idea how a diagram looks like I am not an engineer, however, I can solve equations.

    b) \frac{d^2-d^2\cos^2A}{d^2-d^2\sin^2A}=(9/400).
    Now this problem want to factored thus,

    \frac{d^2(1-\cos^2A)}{d^2(1-\sin^2A)}=9/400
    Thus,
    \frac{1-\cos^2A}{1-\sin^2A}=9/400.
    By the Pythagorean Identities,
    \frac{\sin^2A}{\cos^2A}=\left(\frac{\sin A}{\cos A}\right)^2=9/400
    By the reciprocal identities,
    (\tan A)^2=\tan^2A=9/400
    Thus,
    \tan=\pm 3/20

    Now just use the one your need (the positive one or negative one) and use the inverse-tan on calculator.
    Q.E.D.
    Last edited by ThePerfectHacker; February 2nd 2006 at 02:00 PM.
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  3. #3
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    Thumbs up diagram

    The diagram part of this problem would just be the circle gragh with a right tiangle in it like usual (in the first quadrant i believe) and labeled.
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