Question

The perimeter of a rhombus is $96cm$ and obtuse angle of its is ${120}^{\circ }$. Find the length of its diagonals.

Answer 1

if $\theta$ is the obtuse angle and $s$ be the side of a rhombus then the lengths of the diagonals are $2s\sin (\frac{\theta }{2}),2s\cos (\frac{\theta }{2})$

$2\left(24\right)\left(\sin {60}^{\circ }\right),2\left(24\right)\left(\cos {60}^{\circ }\right)=24\sqrt{3},24$