In a rectangular trapezoid with an acute angle of 60 degrees, the larger side and the larger base

In a rectangular trapezoid with an acute angle of 60 degrees, the larger side and the larger base are equal to 20 cm. Find the smaller base.

1. A, B, C, D – the tops of the trapezoid. CD = 20 cm – large side. AD = 20 cm – more warp. Angle D = 60 °.

2. From the top of C we draw the height of CH to the base of AD.

3. Angle DСН = 180 ° – 60 ° – 90 ° = 30 °.

4. The segment DH, which is the leg in this triangle, located opposite the angle 30, is equal to 1/2 of the hypotenuse CD:

DН = 20: 2 = 10 cm.

5.AH = AD – DH = 20 – 10 = 10 cm.

6. AH = BC as opposite sides of the rectangle ABCH. BC = 10 cm.

Answer: the length of the BC – the smaller base of the trapezoid is 10 cm.