In the MCDE rhombus, the CE diagonal is 12 cm, and the CDE angle is 120 °. Find the height of the diamond.

Let’s draw the second diagonal. О is the intersection point of the diagonals. Since the diagonals of the rhombus are mutually perpendicular, the DOE triangle is rectangular.
Consider a triangle EOD in it the angle EDO = 60º, since the diagonals in the rhombus are bisectors.
So the angle DEO = 90º – 60º = 30º.

In a right-angled triangle, the leg lying opposite an angle of 30º is equal to half the hypotenuse.

Let DO – X, then DE – 2X.

By the Pythagorean theorem 4x ^ 2 – x ^ 2 = 36.

3x ^ 2 = 36

x ^ 2 = 36: 3

x ^ 2 = 12

Height is 3