# The sides of the trapezoid form corners of 60 with the lower base.

**The sides of the trapezoid form corners of 60 with the lower base. The height of the trapezoid is 2 root of 3, and the middle line is 8. Find the lengths of the bases of the trapezoid?**

Let’s draw the height BH of the trapezoid ABCD.

In a rectangular triangle ABH, the angle BAH = 60, then tg60 = BH / AH.

AH = BH / tg60 = 2 * √3 / √3 = 2 cm.

Since the angles at the base of the trapezoid are equal, the trapezoid is isosceles, which means that DP = AH = 2 cm.

Then BC = НР = АD – 4 cm.

According to the formula of the middle line of the trapezoid (BC + AD) / 2 = 8.

BC + AD = 16.

BC = AD – 4.

Let’s solve a system of two equations.

AD + AD – 4 = 16.

2 * AD = 20.

AD = 20/2 = 10 cm.

BC = 10 – 4 = 6 cm.

Answer: The lengths of the bases of the trapezoid are 10 cm and 6 cm.