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Math Help - Problems with Sine Rule Calculations

  1. #1
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    Problems with Sine Rule Calculations

    Hi everyone,

    I am working with the Sine Rule at the moment, where you need to solve the Sine Rule equation to find the value of the unknown side of the triangle. However, although I believe my methods for solving the equation are sound, after performing the calculations themselves, I am left with answers that are sometime a far cry from the correct answer.

    Here is an example:

    I have a triangle with sides MNP. M has an angle of 38 degrees, N has an angle of 80 degrees and P has an angle of 62 degrees. We're given one unknown "x", and one side length which corrosponds to angle N and has a value of 35.3.

    Here is an attachment with a sketch of the triangle: Problems with Sine Rule Calculations-sine-rule-q.jpg

    Now, the Sine Rule is:

    a / Sin A = b / Sin B

    So, I put my values in and get:

    x / sin 38 = 35.3 / sin 80

    I rearrange the equation:

    x = (35.3 / sin 80) x sin 38

    x = 16.76

    The correct answer ought to be: x = 22.1

    I've checked numerous times to ensure my calculator is in degrees mode.

    Any help resolving this will be greatly appreciated!

    Thanks,

    Nathaniel
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  2. #2
    Senior Member Educated's Avatar
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    Really? You must be doing something wrong with your calculator...

    I typed in x = (\frac{35.3}{\sin 80}) \times \sin 38 and i got x = 22.068114... in degrees mode.

    In radians, i got x = -10.5261...

    I'm not sure how you are getting 16.67.
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  3. #3
    Super Member
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    Hi!

    It is probably the way you entered it in the calculator. Your equations are correct.

    Check this:

    (35.3sin38) = 21.7328...

    21.328.../sin80 = 22.068...
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  4. #4
    Junior Member
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    Ah. Thanks for the quick aid Gusbob, and Educated! It WAS just a calculator problem. I didn't realize you have to put the 38 and the 80 before the sine sign (with the online and inbuilt Microsoft calculators that I am using).

    Cheers!
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