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Math Help - Trig Word Problem

  1. #1
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    Trig Word Problem

    Hi, I'm having trouble visualizing this problem. I cant seem to figure out where the measurements should be going.

    "The longer sides of a triangular park measure 251.0m and 208.m respectively. The angle between the longest and shortest side is 56 degrees.

    a) What is the angle between the shorter two sides of the park?
    b) How long is the shortest side?

    I cant seem where to figure out where the 56 degrees go. Between 251 and 208m or between 251 and "x"? From knowing that I'm quite sure I can figure out the problem.
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  2. #2
    Junior Member mathbyte's Avatar
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    Post Re: Trig Word Problem

    The first sentence says that the longer sides measure 251.0m and 208.m (208.0?) respectively.
    Thus, you know "x" is the shortest side.
    That said, you can look at where the 56 degree angle is supposed to go, and it sounds like you have it from there.
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  3. #3
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    Re: Trig Word Problem

    Still a bit confused so it should look something like this?

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  4. #4
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    Re: Trig Word Problem

    Quote Originally Posted by Robert12 View Post
    Still a bit confused so it should look something like this?

    "The longer sides of a triangular park measure 251.0m and 208.m respectively. The angle between the longest and shortest side is 56 degrees.
    is your 56 degree angle between the longest and the shortest side?
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  5. #5
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    Re: Trig Word Problem

    So would it be safe to assume that this is a right angle triangle? If I put the 56 degrees in the top corner I'm able to find the shortest side however that would be the angle between the two shorter sides is 90 degrees if it was right angled. I'm still having trouble visualizing this problem.
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  6. #6
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    Re: Trig Word Problem

    Quote Originally Posted by Robert12 View Post
    So would it be safe to assume that this is a right angle triangle? If I put the 56 degrees in the top corner I'm able to find the shortest side however that would be the angle between the two shorter sides is 90 degrees if it was right angled. I'm still having trouble visualizing this problem.
    no, you cannot assume the triangle is right.

    what do you know about the law of cosines?
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  7. #7
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    Re: Trig Word Problem

    Here is what I have with law of cosines:

    251^2 + 208^2 - 2(251)(208) cos 56
    = 63001 + 43264 - 104416 cos 56
    = 106265 - 58388
    = 218 after square root.

    So 208m is the shortest side not "x".
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  8. #8
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    Re: Trig Word Problem

    Quote Originally Posted by Robert12 View Post
    "The longer sides of a triangular park measure 251.0m and 208.m respectively. The angle between the longest and shortest side is 56 degrees.

    a) What is the angle between the shorter two sides of the park?
    b) How long is the shortest side?
    reviewing the original problem statement, I've come to the conclusion that the given conditions do not lead to a clearly "shortest" side.

    251\sin(56^\circ) \approx 208.09 ... this means that a triangle is not possible with the given sides and conditions as stated in the problem.

    I suspect the problem's author wanted to make it a right triangle (approximately 208.09 would do just that) , but rounded down. That was his/her error.
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