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13 January, 19:31

If the length of side a is 12 centimeters, mZB = 36°, and mZC = 75°, what is the length of side b?

Round your response to two decimal places.

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  1. 13 January, 20:58
    0
    b = 7.56 cm

    Step-by-step explanation:

    Sum of the angles in a triangle = 180

    so m∠A = 180 - 75 - 36 = 69;

    use the law of sines:

    (sin A) / a = (sin B) / b = (sin C) / C.

    Now plug in ∠A = 69 into formula (sin A) / a = (sin B) / b and solve for b:

    (sin 69) / 12 = (sin 36) / b

    cross multiply:

    b sin 69 = 12 sin 36 divide each side by sin 69

    b = {12 sin 36} / sin 69

    b = (12 sin 36) / sin 69 = 7.555 ...

    b = 7.56
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