# In a parallelogram, the sides are 4 and 6 cm, and the acute angle is 45. Find its smaller diagonal.

A parallelogram is a quadrilateral in which opposite sides are equal and lie on parallel lines.

In order to calculate the length of the smaller diagonal of the parallelogram, we use the formula for the length of the diagonal behind the sides and the angle between them:

d = √a ^ 2 + b ^ 2 – 2ab cosα, where:

d – smaller diagonal;

a, b – sides of the parallelogram;

α is an acute angle of a parallelogram.

cos 45 ° = √2 / 2 ≈ 0.525;

d = √ (4 ^ 2 + 6 ^ 2 – 2 ∙ 4 ∙ 6 ∙ √2 / 2) = √ (16 + 36 – 48 ∙ 0.525) = √ (52 – 25.2) = √26.8 ≈ 5 , 18 cm.

Answer: The length of the smaller diagonal is 5.18 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.