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9 December, 07:19

If measure of angle p = (10x-2), measure of angle o = (3x+9), and measure of angle q = (3x-3), list the lengths of the sides of triangle OPQ from longest to shortest.

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  1. 9 December, 08:49
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    The sum of all angles of a triangle must be equal to 180°

    So we can find the value of x ...

    10x-2+3x+9+3x-3=180

    16x+4=180

    16x=176

    x=11

    So the angles are 108°, 42°, 30°

    Now using the Law of Sines we can solve for all sides.

    (sina/A=sinb/B=sinc/C)

    a/sin30=b/sin42=c/sin108

    However, we would need to know at least one side length to solve for sides a, b, and c numerically, otherwise it can be any multiple of an arbitrary choice for the smallest side. Let a=1 for example:

    b=sin42/sin30, c=sin108/sin30

    b≈1.34, c≈1.90

    a=1, b=1.34, c=1.9

    Anyway ...

    If you are given any side length:

    a/sin30=b/sin42=c/sin108 still holds true and you can solve for the other side lengths ...
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