# The lengths of the sides of the trapezoid are 2 cm and 2 cm, and the lengths of the bases are 5 cm and 7.

August 31, 2021 | education

| **The lengths of the sides of the trapezoid are 2 cm and 2 cm, and the lengths of the bases are 5 cm and 7. Find the corners of the trapezoid.**

Let’s designate the trapezoid as ABCD.

The trapezoid is isosceles, therefore the angles at the upper base are equal and the angles at the lower base are equal, that is, A = D, B = C.

Let’s draw the height of the trapezoid BH.

Consider a right-angled triangle ABN.

AH = (AD – BC) / 2 = (7 – 5) / 2 = 1 cm.

By the sine theorem for a right triangle, and using trigonometric transformations:

cosA = AH / AB = ½.

A = arcos (1/2) = 60º.

Since the sum of the angles of the trapezoid adjacent to the lateral side is 180º, A + B = 180º.

B = 180º – 60º = 120º.

Answer: A = D = 60º, B = C = 120º.

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