Question

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.

Answer 1

28 m

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.