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.

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