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Thread: Finding the height with trig

  1. March 8th 2009, 05:49 PM #1
    jsu03
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    Finding the height with trig

    Hi, can someone help me how to do this problem. Thanks a lot.

    Assume that you are constructing a 20 ft road at 2 % gradient. PLease calculate the height of the road?

    Thanks again for your help!!
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  2. March 8th 2009, 07:35 PM #2
    madmartigano
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    This is a right triangle problem.

    Treat the 20 ft. of road as your hypotenuse.

    \sin \theta = \frac{{opposite}}{{hypotenuse}}

    The opposite side is your height, so:

    \begin{array}{l}<br /> \sin \theta = \frac{{height}}{{road}} \Rightarrow height = road \times \sin \theta \\ <br /> \\ <br /> height = 20ft. \times \sin 2^\circ = 0.7ft. \\ <br /> \end{array}
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