In an isosceles trapezoid, the difference in the lengths of the bases is equal to the length

| February 4, 2021 | education

In an isosceles trapezoid, the difference in the lengths of the bases is equal to the length of the lateral side. what is the greater angle of this trapezoid?

Let the length of the smaller base be equal to X cm, and the length of the larger base equal to Y cm.

Then, by assumption, AB = (AD – BC) = (Y – X) see.

Let’s build the heights of the HВ and CM of the trapezoid.

Quadrangle ВСMН is a rectangle, then НM = BC = X cm.

The segment AH = DM, since the right-angled triangles ABН and DСM are equal in acute angle. Then AH = DM = (Y – X) / 2.

In a right-angled triangle AВН: AН / AB = CosВAН.

CosВAН = ((Y – X) / 2) / (Y – H) = 1/2.

Angle ВAН = 60.

In a trapezoid, the sum of the angles at the lateral side is 180, then the angle ABC = 180 – 60 = 120.

Answer: The larger angle of the trapezoid is 120.



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.