# The sides of the parallelogram are 3 and 8 cm, and one of the corners of the parallelogram is 60 °.

June 27, 2021 | education

| **The sides of the parallelogram are 3 and 8 cm, and one of the corners of the parallelogram is 60 °. Find the large diagonal of the parallelogram.**

The large diagonal of the parallelogram lies against its larger angle.

The sum of the adjacent angles of the parallelogram is 180, then the angle ABC = 180 – BAD = 180 – 60 = 120.

For triangle ABC, apply the cosine theorem.

AC ^ 2 = AB ^ 2 + BC ^ 2 – 2 * AB * BC * Cos120 = 9 + 64 – 2 * 3 * 8 * (-1/2) = 73 + 24 = 97.

AC = √97 cm.

Answer: The length of the larger diagonal is √97 cm.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.