In an isosceles trapezoid, the lateral side is 16 and makes an angle of 60 degrees

| August 12, 2021 | education

In an isosceles trapezoid, the lateral side is 16 and makes an angle of 60 degrees with a large base. the middle line of the trapezoid is 28, find the larger base of the trapezoid

Let’s draw the heights BK and CH of the trapezoid ABCD. In a right-angled triangle ABK, the angle ABK = (90 – 60) = 30. Then the leg AK lies opposite the angle 30, then AK = AB / 2 = 16/2 = 8 cm.

Since the trapezoid is isosceles, the right-angled triangles ABK and CDH are equal in hypotenuse to an acute angle, then DH = AK = 8 cm.

A quadrilateral BСНK is a rectangle, then BC = KH.

AD = AK + KН + DK = 8 + BC + 8 = 16 + BC.

The middle line of the trapezoid is: KM = (BC + AD) / 2 = 28 cm.

(BC + 16 + BC) = 56.

2 * BC = 40.

BC = KH = 40/2 = 20 cm.

AD = 8 + 20 + 8 = 36 cm.

Answer: The length of the larger base is 36 cm.



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