One of the four angles of a rhombus is 60°. If the length of each side of the rhombus is 8 cm, then the length of the longer diagonal is

Solution (By Examveda Team)

Let ∠ABC = 60°
∠OBC = 30°
∴ Diagonals of Rhombus are the angle bisectors
In right ΔBOC
$$\eqalign{ & \frac{{{\text{OB}}}}{{{\text{BC}}}} = \cos {30^ \circ } \cr & \frac{{{\text{OB}}}}{8} = \frac{{\sqrt 3 }}{2} \cr} $$
OB = $$4\sqrt 3 $$
∴ BD = 2 × OB
= 2 × $$4\sqrt 3 $$
= $$8\sqrt 3 $$  cm