Question 118

If ABCD be a rhombus, AC is its smallest diagonal and $$\angle\ $$ABC = $$60^\circ$$, find length of a side of the rhombus when AC = 6 cm.

Solution

Given : AC = 6 cm and $$\angle\ $$ABC = $$60^\circ$$

Diagonals of a rhombus bisect each other at right angle and also bisects the opposite angles.

=> OC = $$\frac{6}{2}=3$$ cm and $$\angle$$ OBC = $$\frac{60}{2}=30^\circ$$

In $$\triangle$$ OBC,

=> $$sin(\angle OBC)=\frac{OC}{BC}$$

=> $$sin(30^\circ)=\frac{3}{BC}$$

=> $$\frac{1}{2}=\frac{3}{BC}$$

=> $$BC=2\times3=6$$ cm

=> Ans - (D)

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