The lateral side of an isosceles trapezoid is 6 cm, the larger base is 10 cm.

The lateral side of an isosceles trapezoid is 6 cm, the larger base is 10 cm. Find the middle side if one of its corners is 60 degrees.

First you need to find the smaller base of the lateral trapezoid.

The size of the larger base is equal to the sum of the size of the smaller base and twice the size of the leg of the right-angled triangle, which forms the height of the trapezoid.

The cosine of the base angle is the ratio of this leg to the side.

cos 60 ° = x / 6;

x = 6 * 1/2 = 3;

The lesser base is equal to:

a = b – 2 * x = 10 – 6 = 4;

The middle line of a trapezoid is the sum of the bases, divided by two:

D = (a + b) / 2 = (10 + 4) / 2 = 7.