The height of the isosceles trapezoid, drawn from the top of C, divides the base of AD

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

Given:
ABCD – isosceles trapezoid,
CH – height,
НD = 8,
AD = 15.
Find the length of the smaller base of the BC -?
Solution:
1) We will carry out more from the top  В to the height of the ВC;
2) Consider a triangle ABK and a triangle CDH. They are rectangular, since CH and BK are tops. These triangular are equal to each other because they have hypotenuse CD = AB and angle A = angle D (ABCD – isosceles trapezoid) along the hypotenuse and acute angle. Therefore, AK = HD = 8;
3) AН = AK + KН;
15 = 8 + KH;
KН = 15 – 8;
KH = 7;
4) BC = KН = 7 (since the quadrangle KBСН is a rectangle).
Answer: 7.