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18 February, 09:17

The diagonals of a parallelogram are 16 meters and 14 meters and intersect at an angle of 60°. find the length of the longer side.

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  1. 18 February, 12:52
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    Refer to the diagram shown below.

    Note that

    (i) the intersecting diagonals of the parallelogram bisect each other;

    (ii) the supplementary angle of 60° is 120°.

    Let

    a = the length of the longer side

    b = the length of the shorter side.

    Apply the Law of Cosines to the lower triangle.

    a² = 8² + 7² - 2 (8) (7) cos (120)

    = 64 + 49 + 56

    = 169

    a = 13 m

    Answer: 13 m
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