Question

If the length of each side of a rhombus is $8$ $cm$ and one angle is ${60}^{\circ }$ then find the length of diagonal.

Answer 1

In the rhombus $PQRS,\angle S={60}^o\Rightarrow \angle R=120,SR=8cm$

$S{Q}^2=S{R}^2+Q{R}^2-2\left(QR\right)\left(SR\right)cos\left({120}^o\right)$

$S{Q}^2=8^2+8^2-2\left(8\right)\left(8\right)\left(\frac{-1}{2}\right)$

$=8^2[1+1+1]$

$\therefore SQ=8\sqrt{3}$

$SQ=8\sqrt{3}cm$