Math

In a triangle ABC, with angles A, B, and C and sides AB, BC, and AC, angle B is a right (90°) angle. If the sin of angle A is 0.5 and side BC is 8 inches long, what is the length of side AC?

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  1. sin A = 1/2
    A = 30 degrees

    sin is opposite over hypotenuse thus, BC/AC
    BC = 8 (given)

    thus 1/2 = 8/AC
    AC = 16

    cos A is cos 30degrees so cos A = (sqrt(3)) / 2

    cos is always adjacent over hypotenuse thus, AB/AC
    because AC = 16

    sqrt3 /2 = AB/16

    AB = 8 sqrt3

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