The height of an isosceles trapezoid drawn from the vertex C divides the base of AD into segments

The height of an isosceles trapezoid drawn from the vertex C divides the base of AD into segments of length 8 and 15. Find the length of the base of BC.

Solution: to solve this problem, we need to additionally draw the height from point B (if the trapezoid is ABCD) to the base AD. Let’s denote the point to which the height is drawn from the point by the letter M, and the height drawn from the point C by the letter T. Since the trapezoid is isosceles, a rectangle BCTM is formed. DT = AM = 8, since AT = 15 (according to the problem statement), then TM = TA – MA = 15 – 8 = 7. BC = MT = 7, since they are in the BCTM rectangle and are parallel.
Answer: the length of the base BC = 7.