Adjacent sides of the parallelogram = 3cm and 4cm, the angle between them is 120

Adjacent sides of the parallelogram = 3cm and 4cm, the angle between them is 120, find the length of the smaller diagonal of the parallelogram.

The length of the smaller diagonal d will depend on the smaller angle of the parallelogram, which is: <A = (180 ° – 120 °) = 60 °., And on its two sides a and b. We use the formula for determining any side in a triangle using the cosine of the angle, and two other sides, where a and b are the sides of the parallelogram. (Sides a, b, and d make up a triangle with an angle A = 60 °).

d ^ 2 = a ^ 2 + b ^ 2 + 2 a * b * cos <A = 3 ^ 2 + 4 ^ 2 + 2 * 3 * 4 * cos (60 °) = 9 + 16 + 24 * 1/2 = 25 + 12 = 37 (cm ^ 2).

The smaller diagonal d is equal to:

q = √ (37) cm.