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Find all solutions for a triangle with a = 6, b = 8, and A = 150°

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  1. 5 May, 03:47
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    6/sin 150 = 8 / sin B

    Step-by-step explanation:

    6/sin 150 = 8 / sin B

    sin 150 = 1/2 so you cross multiply to get 6 sin B = (1/2) • 8

    6 sin B = 4

    sin B = 4/6

    B = inverse sin (4/6) = 42º or 138º

    But both of those add to 150 to go over 180 so there are no solutions.

    Back in geometry, you had that the larger angle of a triangle is opposite the longer side, right? You can see that 150º can't be opposite 6 because then the angle opposite 8 would have to be larger than 150º which is impossible for a triangle.
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