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Math Help - Cosine Law Problem

  1. #1
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    Post Cosine Law Problem

    The longest tunnel in North America could be built through the mountains of the Kicking Horse Canyon, near Golden, British Columbia. The tunnel would be on the Trans-Canada highway connecting the Prairies with the west coast. Suppose the team selected point A, 3000m away from the proposed tunnel entrance and 2000m away from the tunnel exit. If angle A is measured 67.7 degrees, determine the length of the tunnel.

    So, I tried doing this question using the formula:

    a^2 = b^2 + c^2 - (2)(b)(c)cosA

    I drew a diagram of how I think the problem would look like aswell:



    My attempt:

    a^2 = b^2 + c^2 - (2)(b)(c)cosA

    a^2 = 2000^2 + 3000^2 - (2)(2000)(3000)cos67.7


    a^2 = 13000000 - 12000000cos67.7


    a^2 = 1000000cos67.7


    a^2 = 379456.1595

    a = 616 m

    The answer is suppose to be 2906 m... I'm not sure what I did wrong... Any feedback would be great, thanks.
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  2. #2
    Senior Member Paze's Avatar
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    Re: Cosine Law Problem

    Hi Mathnood768.

    Your calculations are right. You are stumbling in the arithmetic.

    For proof that your calculations are right, see: sqrt(2000^2+3000^2-2*2000*3000*cos(67.7)) - Wolfram|Alpha

    Try and see where your arithmetic is foiling your solution.
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  3. #3
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    Re: Cosine Law Problem

    I got it!!! Thanks for clarifying!
    Last edited by Mathnood768; March 17th 2013 at 07:33 PM.
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