If the side of the rhombus is equal to a, one of its angles is 120 degrees, then what will its diagonals be equal to?

As we know from the school curriculum in geometry, the diagonals in such a geometric figure will be perpendicular to each other, that is, they will form right-angled triangles.

Let us determine through what number of degrees one of the acute angles in such a triangle will be expressed, if from the condition of the task we know that the angle of the rhombus is 120 °:

120: 2 = 60.

The halves of the diagonals are the legs of such a triangle, we find them:

cos 60 ° = 1/2;

a * 1/2 = a / 2;

sin 60 ° = √3 / 2;

a * √3 / 2 = a√3 / 2.

Then the diagonals are equal to a and a√3.

Answer: a and a√3.