The diagonals of a parallelogram are 24 meters and 40 meters and intersect at an angle of 60o. Find the length of the longer side.

  28 m

Step-by-step explanation:

The longer side can be found using the Law of Cosines. The semi-diagonals are of length 12 and 20 m, and the angle between them facing the long side is 180° -60° = 120°.

  c^2 = a^2 +b^2 -2ab·cos(C)

  c^2 = 12^2 +20^2 -2·12·20·cos(120°) = 144 +400 +240 = 784

  c = √784 = 28

The longer side is 28 meters.

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