The sides of the parallelogram are 3 cm and 8 cm, and one of the angles is 60 degrees.

The sides of the parallelogram are 3 cm and 8 cm, and one of the angles is 60 degrees. Find the large diagonal of the parallelogram.

A parallelogram is a quadrilateral in which the opposite sides are pairwise parallel and equal to each other.

In order to find the large diagonal of the parallelogram, we use the formula for the area behind the sides and the angle between them:

D = √ (a ^ 2 + b ^ 2 + 2ab ∙ cosα); where:

D – large diagonal;

a, b – sides of the parallelogram;

α is the angle between the sides of the parallelogram.

cos 60º = 1/2 = 0.5;

D = √ (3 ^ 2 + 8 ^ 2 + 2 ∙ 3 ∙ 8 ∙ 0.5) = √ (9 + 64 + 24) = √97 ≈ 9.85 cm.

Answer: The length of the larger diagonal of the parallelogram is 9.85 cm.