The sides of the parallelogram are 5 cm and 8 cm, the angle between them is 120 degrees.

The sides of the parallelogram are 5 cm and 8 cm, the angle between them is 120 degrees. Find the diagonals of the parallelogram.

Angle ABC = 120 degrees
Angle BCD = 180 – 120 = 60 degrees

Let’s apply the cosine theorem to find the diagonals:
AC ^ = AB ^ + BC ^ – 2 * AB * BC * cos (ABC)
AC ^ = 64 + 25 – 80 * (-0.5) = 129
AC = √ (129)

BD ^ = BC ^ + CD ^ – 2 * BC * CD * cos (BCD)
BD ^ = 64 + 25 – 80 * 0.5 = 49
BD = 7

Answer: √ (129), 7.