# The diagonals of the rectangle are 28 cm. The angle between them is 60 degrees. find the smaller side of the rectangle.

September 27, 2021 | education

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

AC = BD = 28 cm.

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

AO = BO = 28: 2 = 14 cm. ∠AOB = ∠ABO.

3. The degree measure of each of them is (180 ° – 60 °) / 2 = 60 °, that is, the AOB triangle is equilateral.

Therefore, AB = BO = AO = 14 cm.

Answer: AB = 14 cm – the smaller side of the rectangle.

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