The sides of the trapezoid ABCD intersect at right angles as it continues Find AB if the angle is BAD

The sides of the trapezoid ABCD intersect at right angles as it continues Find AB if the angle is BAD = 28 degrees; BC = 8cm; AD = 12cm

Since the continuation of the lateral sides intersect at right angles, the triangles AED and BEC are rectangular and similar in acute angle, since the angle EAC = EBC as the corresponding angles at the intersection of parallel AD and BC secant AE.

The coefficient of similarity of triangles is: K = BC / AD = 8/12 = 2/3.

Segment length BE = BC * Cos28.

BE / AE = 2/3.

AE = 3 * BE / 2 = 3 * 8 * Cos28 / 2 = 12 * Cos28.

Then AB = AE – BE = 12 * Cos28 – 8 * Cos28 = 4 * Cos28.

Answer: The length of the AB side is 4 * Cos28.