The sides of the parallelogram are 3 and 5 cm, and the angle between them is 60 degrees.

The sides of the parallelogram are 3 and 5 cm, and the angle between them is 60 degrees. Find the length of the larger diagonal of the parallelogram.

Since ABCD is a parallelogram, AB = CD = 3 cm, BC = AD = 5 cm.

A parallelogram has the sum of its adjacent angles equal to 180.

Then the angle ADC = (180 – BAD) = (180 – 60) = 120.

In the triangle ACD, by the cosine theorem, we define the side AC.

AC ^ 2 = AD ^ 2 + CD ^ 2 – 2 * AD * CD * Cos120 = 25 + 9 – 2 * 5 * 3 * (-1/2) = 34 + 15 = 9.

AC = 7 cm.

Answer: The length of the larger diagonal is 7 cm.