The side of the rhombus is 20, and the acute angle is 60 degrees. Find the length of the smaller diagonal.

univerkov | September 14, 2021 | education

The diagonals of the rhombus are bisectors of the angles at the vertices, then the angle ABO = BAD / 2 = 60/2 = 30. The diagonals at the intersection point are halved and intersect at right angles. Then, in the ABO triangle, the BO leg lies opposite the angle 30 and is equal to half the length of AB. BО = 20/2 = 10.

BD = 2 * BO = 2 * 10 = 20 cm.

Answer: The length of the smaller diagonal is 20 cm.

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