Find the side of an equal trapezoid, its base equal to 12 and 6 cm. One of the three angles is equal to 60 degrees.

Given:

isosceles trapezoid ABCE,

BC = 6 centimeters,

AE = 12 centimeters,

angle A = angle E = 60 degrees.

Find the length of the side, that is, AB -?

Solution:

1. Consider an isosceles trapezoid ABCE. Let’s draw the heights BH and CO. We get the HBCO rectangle. He has BH = CO and BC = HC = 6 centimeters.

2. Right-angled triangle AH = right-angled triangle COE along the hypotenuse and acute angle, since angle A = angle E and CE = AB. Then CE = AH = (12 – 6): 2 = 6: 2 = 3 (centimeters).

3. Consider the BHA triangle. Angle ABH = 180 – 90 – 60 = 30 (degrees). The leg, which lies opposite an angle of 30 degrees, is equal to half of the hypotenuse, that is, AB = 2 * AH = 2 * 3 = 6 (centimeters).

Answer: 6 centimeters.