ABCD is an isosceles trapezoid. BC = 2, AD = 20, BA = CD = 15. Find angle A and angle B.

A trapezoid is a quadrilateral in which one pair of opposite sides is parallel, and the sides are not equal to each other.

Isosceles is a trapezoid in which the sides are equal.

In an isosceles trapezoid, the segment of the larger base located between its heights is equal to the length of the smaller base:

HK = BC.

Thus:

AH = KD = (AD – HK) / 2;

AH = KD = (20 – 2) / 2 = 18/2 = 9 cm.

In order to calculate the length of the BH height, consider the triangle ΔABH.

This triangle is rectangular. To calculate, we use the Pythagorean theorem, according to which, the square of the hypotenuse is equal to the sum of the squares of the legs:

AB ^ 2 = BH ^ 2 + AH ^ 2;

BH ^ 2 = AB ^ 2 – AH ^ 2;

BH ^ 2 = 15 ^ 2 – 9 ^ 2 = 225 – 81 = 144;

BH = √144 = 12 cm.

Answer: The length of the HV height is 12 cm.