One of the corners of a rectangular trapezoid is 30 degrees. Large lateral side 24 cm. Find the smaller lateral side of the trapezoid.

Let’s designate our trapezoid as ABCD AB, CD – the sides, smaller and larger, respectively, BC, AD – the bases of the trapezoid. Let’s draw the height CL, its length will be equal to the length of the smaller lateral side, consider the right-angled triangle CLD:

sin (CDL) = CL / CD, where the CDL angle is a 30-degree angle.

CL = CD * sin (CDL) = 24 * (1/2) = 12 cm.

Since it was said that the length CL and the length AB are equal, then the length AB is 12 cm.

Answer: the length of the smaller side of the trapezoid is 12 cm.