The diagonal of the rectangle is 10 cm. the angle between the diagonals is 60 °.

univerkov | May 4, 2021 | education

The diagonal of the rectangle is 10 cm. the angle between the diagonals is 60 °. calculate the side of the smaller side of the rectangle.

According to the property of the diagonals of the rectangle, their lengths are equal to each other, AC = BD = 10 cm, and at the point of their intersection they are divided in half OA = OB = OC = OD = AC / 2 = 10/2 = 5 cm.

Since ОА = ОВ = 5 cm, therefore, triangle AOB is isosceles, one of the angles of which is 60. Then the angle ОАВ = ОВА = (180 – 60) / 2 = 60, therefore, triangle ABO is equilateral, AB = ОВ = ОА = 5 cm.

Answer: The length of the shorter side is 5 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.