Given a rhombus with an angle of 120 degrees and a side equal to 5.3 m. Find the smaller diagonal of the rhombus.

The diagonal of the rhombus AC divides it into two equal isosceles triangles. Consider a triangle ΔABС.

The angle BAC is equal to 60 °, since the diagonal of the rhombus is the bisector of its angles and divides them in half, and the angle A is equal to 120 °:

∠BAC = 120 ° / 2 = 60 °.

In an isosceles triangle, the angles at the base are equal, therefore:

∠ВСА = ∠ВСА = 60 °.

Since the sum of all the angles of the triangle is 180 °, then:

∠ABС = 180 ° – ∠BCA – ∠BAC;

∠ABС = 180 ° – 60 ° – 60 ° = 60 °

Based on this, we see that this triangle is regular and all its sides will be the same. Therefore, the AC diagonal is equal to the AB side:

AC = AB = BC = 5.3 cm.

Answer: The smaller diagonal of the rhombus is 5.3 cm.