SSC CHSL 15 Nov 2015 Shift 2 Paper

Question : 118 of 200

Marks: +1, -0

If ABCD be a rhombus, AC is its smallest diagonal and ∠ABC = 60° , find length of a side of the rhombus when AC = 6 cm.

Solution:

Given : AC = 6 cm and ∠ABC = 60°
Diagonals of a rhombus bisect each other at right angle and also bisects the opposite angles.
⇒ OC =

6/2=3

cm and ∠OBC =

60/2=30°

In ∆OBC,
⇒

sin(∠OBC) = {OC}/{BC}

⇒

sin(30°) =3/ {BC}

⇒

1/2=3/{BC}

⇒

BC = 2 × 3 = 6

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