Math

A parallelogram ABCD has lengths of sides and angles given below. Find the length of the diagonals AC and BD. (Round your answers to two decimal places.)
AB = DC = 6 and AD = BC = 3, A = 40°

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  1. A = C = 40deg.

    B = D = (360-80) / 2 = 140 deg.

    Using the Law of signs,
    BD / sinA = AB / sin(D/2),
    BD / sin40 = 6 / sin70,
    Multiply both sides by sin40:
    BD = 6sin40 / sin70 = 4.1.

    AC / sinD = AD / sin(C/2),
    AC / sin140 = 3 / sin20,
    AC = 3sin140 / sin20 = 5.64.

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