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Math Help - Triangle measurements

  1. #1
    Newbie
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    Triangle measurements

    Triangle

    xz=18.5 m
    xy=12.2 m
    ∠x= 73

    use the given measurements to find each of the following:
    A. YZ
    B. M
    ∠XZY
    C. M∠xyz
    D. The area
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  2. #2
    MHF Contributor
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    This is a classic case for the law of cosines and the law of sines.

    Let XZ = a, XY = b, YZ = c. Then, by the law of cosines:

    c^2 = a^2 + b^2 - 2ab \cos 73.

    After you calculate c, then use the law of sines to find the angles:

    \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin 73}
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  3. #3
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    How do you find yz?
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  4. #4
    MHF Contributor
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    I defined the length of YZ as c. Since you know the lengths of XZ (a) and XY (b), and the measure of the angle they share (ZXY = C = 73 degrees), you can use the law of cosines to find the length of YZ (c).
    The calculation is c^2 = (18.5)^2 + (12.2)^2 - 2(18.5)(12.2)\cos 73.
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