In a rectangular trapezoid, the acute angle is 60 degrees, the large lateral side is equal to 20 cm, find a smaller base.

From the top of the obtuse angle C of the trapezoid, we lower the height of CH to the base of AD.

In the formed right-angled triangle СDН, the НDС angle, by condition, is 60, then the DСН angle = 180 – 90 – 60 = 30.

Then the length of the leg of the DН, which lies opposite the angle 30, is equal to half the length of the hypotenuse of the DM.

DН = СD / 2 = 20/2 = 10 cm.

The segment AH the base of the trapezoid AD is equal to: AH = AD – DН = 20 – 10 = 10 cm.

Quadrangle ABCН is a rectangle, since BC is parallel to AH as the base of the trapezoid, AB is parallel to CH, since CH is the height of the trapezoid, and AB is perpendicular to AH by condition. Then BC = AH = 10 cm.

Answer: The smaller base is 10 cm.