The side of the rhombus is a, one of its corners is 120 degrees. Find the diagonals of the rhombus.

Decision:
We have a rhombus, the diagonals in the rhombus divide the angle in half, which means if we draw both diagonals, we get four right-angled triangles, in which the hypotenuse = a, and the angles are 90 °, 60 °, 30 °.
The leg, lying opposite the angle of 30 ° is equal to half of the hypotenuse, which means we get a triangle with leg a / 2 and hypotenuse a.
Further, by the Pythagorean theorem, we find the second leg, which will be equal to √3 * a / 2.
The diagonals at the intersection are halved. We know half of them, which means the answer is:
d1 = a
d2 = √3 * a.