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Math Help - triangle help

  1. #1
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    triangle help

    Let the sides of a triangle have the respective lengths a=3, b=5,c=6. The respective angles opposite a, b, and c have A, B, and C radian measures.

    Using your graphing calculator determine A, B, and C rounded off to six digits to the right of the decimal point. Verify your answers by checking whether A+B+C = ∏. Explain any discrepancy. I'm having a tough time figuring this out .. Please help.
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  2. #2
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    Do you know the law of cosines?
    Can you use the arccosine function?
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  3. #3
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    Quote Originally Posted by Tazsweet19 View Post
    Let the sides of a triangle have the respective lengths a=3, b=5,c=6. The respective angles opposite a, b, and c have A, B, and C radian measures.

    Using your graphing calculator determine A, B, and C rounded off to six digits to the right of the decimal point. Verify your answers by checking whether A+B+C = ∏. Explain any discrepancy. I'm having a tough time figuring this out .. Please help.
    Using law of cosine,

    cos A = \frac {b^2 +c^2 -a^2}{2bc}

    cos A = \frac {5^2+6^2-3^2}{2\times 5 \times 6}

    cos A = \frac {52}{60}

    cos A = 0.866666667

     A = 0.522315 \ radians

    In the same way,

    cos B = \frac {a^2 +c^2 -b^2}{2ac}

    cos B = \frac {3^2+6^2-5^2}{2\times 3 \times 6}

    cos B = \frac {20}{36}

    cos B = 0.555555556

     B = 0.981765 \;radians

    Now, calculate for angle C

    cos C = \frac {a^2 +b^2 -c^2}{2ab}

    cos C = \frac {3^2+5^2-6^2}{2\times 3 \times 5}

    cos C = \frac {-2}{30}

    cos C = -0.0666666667

     C = 1.637512 \ radians

    Now check,

    A + B + C = 0.522315 + 0.981765 + 1.637512

    = 3.141592 radians

    = \pi \; radians

    So, A+B+C = \pi \; radians

    Since the actual value of  \pi = 3.1415926536 but rounded off for six digits, it is 3.141593 and our answer is 3.141592, so the difference between actual value and our answer is 0.000001, that is negligible.
    Last edited by Shyam; September 6th 2008 at 01:06 PM.
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  4. #4
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    Yes I learn law of cosine before I got to anwer - = 0.86666 then cosA = 0.86666. then how do i convert it to degrees? If I keep going to Cos B and Cos C. I will figure out it.
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  5. #5
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    Quote Originally Posted by Tazsweet19 View Post
    Yes I learn law of cosine before I got to anwer - = 0.86666 then cosA = 0.86666. then how do i convert it to degrees? If I keep going to Cos B and Cos C. I will figure out it.
    you got cos A = 0.86666

    A= 0.5222328 radians

    to make into degrees multiply with \frac {180}{\pi}

    A= 0.5222328 \times \frac {180}{\pi}

    A= 29.9 \; degrees

    because; \;  \boxed{ \pi \; radians = 180 \; degrees}

    So,\;  1 \; radian = \frac {180}{\pi} \; degrees

    So,\;  0.5222328 \; radians = 0.5222328 \times \frac {180}{\pi} \; degrees
    Last edited by Shyam; September 6th 2008 at 08:00 PM.
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