In trapezoid ABCD, the base of AD is perpendicular to the side of AB, the diagonal of AC is perpendicular to the side of CD

In trapezoid ABCD, the base of AD is perpendicular to the side of AB, the diagonal of AC is perpendicular to the side of CD. Find the length of the side of the CD if BC = 6cm, angle BCA = 30 degrees.

In a right-angled triangle ABC, the length of the BC leg is 6 cm, and the BCA angle = 30, then the length of the hypotenuse AC = BC / Cos30 = 6 / (√3 / 2) = 12 / √3 = 4 * √3 cm

Angle DАС = АСВ = 30 as criss-crossing angles at the intersection of parallel lines АD and ВС secant АС. Determine the length of the leg CD from the right-angled triangle ACD.

tgCAD = CD / AC.

СD = tg30 * AC = (1 / √3) * 4 * √3 = 4 cm.

Answer: The length of the side of the CD is 4 cm.