You are given a rectangular trapezoid with bases of 4 cm and 7 cm and an angle of 60 degrees. Find a large side.

univerkov | April 10, 2021 | education

From the top of the obtuse angle C of the trapezoid, draw the height of CH to the base of AD. In the formed right-angled triangle СНD, the angle НDС, by condition, is equal to 60, then the angle НСD = 180 – 90 – 60 = 30.

Since the quadrangle ABCN is a rectangle, then AH = BC = 4 cm.Then DH = AD – AH = 7 – 4 = 3 cm.

The leg DH of the triangle CHD lies opposite the angle 30, therefore, it is equal to half the length of the hypotenuse CD. Then CD = DH * 2 = 3 * 2 = 6 cm.

Answer: The large side is 6 cm.

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