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

13 m