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Math Help - Length of Side b

  1. #1
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    Length of Side b

    In ΔABC, m<C = 30 and a = 24. If the area of the triangle is 42, what is the length of side b?

    Is this a law of sines or law of cosines problem?
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  2. #2
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    Quote Originally Posted by magentarita View Post
    In ΔABC, m<C = 30 and a = 24. If the area of the triangle is 42, what is the length of side b?

    Is this a law of sines or law of cosines problem?
    The area of a triangle is calculated by:

    A_{\Delta} = \dfrac12\cdot a\cdot b\cdot \sin(C)= \dfrac12\cdot a\cdot c\cdot \sin(B)= \dfrac12\cdot b\cdot c\cdot \sin(A)

    \sin(30^\circ) = \dfrac12

    Plug in the values you know into the approriate equation:

    A_{\Delta} =\dfrac12\cdot 24\cdot b\cdot \sin(30^\circ)=\dfrac12\cdot 24\cdot b\cdot \dfrac12= 6b

    Therefore

    6b = 42~\implies~\boxed{b = 7}
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  3. #3
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    yes........

    Quote Originally Posted by earboth View Post
    The area of a triangle is calculated by:

    A_{\Delta} = \dfrac12\cdot a\cdot b\cdot \sin(C)= \dfrac12\cdot a\cdot c\cdot \sin(B)= \dfrac12\cdot b\cdot c\cdot \sin(A)

    \sin(30^\circ) = \dfrac12

    Plug in the values you know into the approriate equation:

    A_{\Delta} =\dfrac12\cdot 24\cdot b\cdot \sin(30^\circ)=\dfrac12\cdot 24\cdot b\cdot \dfrac12= 6b

    Therefore

    6b = 42~\implies~\boxed{b = 7}
    Yes, I forgot about those 3 formulas.
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