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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