The height of an isosceles trapezoid is h and the side is visible from the intersection of the diagonals

| April 19, 2021 | education

The height of an isosceles trapezoid is h and the side is visible from the intersection of the diagonals at an angle of 60 degrees. Find the diagonal of the trapezoid.

By condition, the angle AOB = 60. Since the angle AOB and the angle AOD are adjacent angles, and their sum is 180, the angle AOD = 180 – 60 = 120.

ABCD is an isosceles trapezoid, its diagonals at the point of intersection are divided into equal segments, AO = OD, then triangle AOD is isosceles, and angle DAO = ADO = (180 – 120) / 2 = 30.

From the right-angled triangle ВНD, knowing the height ВН and the angle ВDН, we determine the length of the hypotenuse ВD.

Since the height of the ВН lies against the angle 30, its length is equal to half the length of the ВН, then ВD = AC = 2 * ВН = 2 * h cm.

Answer: The length of the diagonals of the trapezoid is 2 * h cm.



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