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Math Help - Percentage error.

  1. #1
    zig
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    Percentage error.

    Please can anyone help solve this? Many Thanks
    The side a of a triangle ABC is calculated from the following formula:


    a/SIN (A) = b/ SIN (B)

    where lower case refers to the sides and upper case refers to the angles opposite those sides. The side b maybe in error by 3.5%

    A=56 degrees
    B- 44 degrees

    Using partial differentiation find the greatest % error in calculated value of a to 5dp

    Thanks
    Last edited by mr fantastic; August 4th 2010 at 05:16 PM. Reason: Re-titled.
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  2. #2
    A Plied Mathematician
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    If you look here, you will find some useful information. With your linear relationship, it should be rather straight-forward to compute what you need. What have you done so far?
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  3. #3
    zig
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    Hi Ackbeet. Have not managed to get very far at all. Have tried putting given figures into examples but cannot seem to work it out. If you know the answer to this question and could show how you calculated the answer I would be very grateful.
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  4. #4
    A Plied Mathematician
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    It's a linear relationship between a and b. That is,

    \displaystyle{a=b\,\frac{\sin(A)}{\sin(B)}}.

    If you take the partial derivative, you get

    \displaystyle{\frac{\partial a}{\partial b}=\frac{\sin(A)}{\sin(B)}}.

    Therefore, the percent errors of a and b are related how?
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  5. #5
    zig
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    Many Thanks for this but could you also provide the answer to the question?
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  6. #6
    A Plied Mathematician
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    could you also provide the answer to the question?
    That's not the way we operate around here. In this forum, we don't hand out the answers. We help you get unstuck, perhaps. You're supposed to do the work, the heavy lifting. This is all for your benefit. Remember the Chinese proverb:

    Tell me, and I forget. Show me, and I remember. Make me do it, and I understand.

    Understanding is what's going to be truly useful for you.

    This problem is really almost done. What would you do next?
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  7. #7
    zig
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    This is what I have managed to do and keep getting the answer as 3.5% which I know is incorrect as the system is marking my answer as incorrect.

    da = [sin(A)/sin(B)] db
    da/a = [sin(A)/(a sin(B))] db = [b sin(A)/(a sin(B))] db/b

    multiply both sides of the Law of Sines result by sin(A) sin(B), you get

    a sin(B) = b sin(A)

    so

    b sin(A) / (a sin(B)) = 1

    Therefore,

    da/a = db/b

    I am clearing doing something wrong. Thanks
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  8. #8
    A Plied Mathematician
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    Your computation for the relative error seems correct to me. See here for a verification.

    I guess this is my question: are you sure the problem is asking for percent error? Or is it asking for absolute error?
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