The smaller side of the rectangle is 5cm. Its diagonals intersect at an angle of 60 degrees. Find the lengths of the diagonals.

1. A, B, C, D – the vertices of the rectangle. ∠АВ = 60 °. О is the point of intersection of the diagonals. AB = 5 cm.

2. Triangle AOB – isosceles, since the diagonals of the rectangle are equal and at the point of intersection are divided into equal segments.

∠AOB = ∠ABO

3. Since the sum of the angles of this geometric figure is 180 °, the degree measure of each of them is 60 °, that is, the triangle AOB is equilateral.

Therefore, AB = BO = AO = 5 cm.

Diagonals BD = AC = 5 x 2 = 10 cm.

Answer: diagonals BD = AC = 10 cm.