The rectangle ABCD and the rhombus have a common side AD, point C lies on the side of the CM.

The rectangle ABCD and the rhombus have a common side AD, point C lies on the side of the CM. Find the length of side AB if AD = 4, angle KAD = 30 °.

Angle KAD = angle AKB = 30 °, as internal cross-lying angles when sectioning parallel lines AD and BC.
Angle DMC = angle AKB = 30 °, as the corresponding angles when sectioning parallel straight lines AK and DM.
Consider triangle DCM and define the DC side.
DM = AD = 4 cm as sides of a rhombus.
Sin DMC = DC / DM;
DC = DM * Sin 30 °;
DC = 4 * 0.5 = 2 cm.
DC = AB = 2 cm.
Answer: the side of the rectangle AB = 2 cm.