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14 December, 10:59

The lengths of two adjacent sides of a parallelogram are 6 and 14. If the measure of an included angle is 60, find the length of the shorter diagonal of the parallelogram.

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  1. 14 December, 11:48
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    Let the name of the parallelogram be ABCD, the two adjacent sides of the parallelogram be AB and AD. AB=14 and AD = 6. The shorter diagonal of parallelogram is BD. The angle between AB and AD is 60.

    In triangle ABD, according to the cosine rule,

    BD^2=AB^2+AD^2-2 (AB) * (AD) cos (60)

    = 14^2+6^2 - (2) 14) (6) (0.5)

    =196+36-84

    = 232-84

    =148

    BD^2=148

    BD=12.1655

    So the length of the shorter diagonal is 12.1655 unit.
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