**If the length of each side of a rhombus is 8 cm and its one angle is 60****°****, then find the lengths of the diagonals of the rhombus.**

**Answer :**

Each side of a rhombus = 8 cm

One angle = 60°

∠OAB = 60°/2 = 30°

In right ∠AOB

sin 30° = OB/AB

½ = OB/8

OB = 8/2 = 4 cm

BD = 2OB = 2 × 4 = 8 cm

cos 30° = AO/AB

√3/2 = AO/8

AO = 8√3/2 = 4√3

AC = 4√3 × 2 = 8 √3 cm

Hence,

The length of the diagonals of the rhombus are 8 cm and 8√3 cm.

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