Question

A rhombus has sides of length 1 cm and the area $\frac{1}{2}{cm}^2$. Find the angle between the two adjacent sides of the rhombus.

• A. ${60}^{\circ }$
• B. ${75}^{\circ }$
• C. ${45}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

The correct option is D ${30}^{\circ }$

Let $ABCD$ be rhombus

The base of Rhombus $BC=$ $1cm$

The area of rhombus is $base\times height=\frac{1}{2}Height\left(AE\right)=\frac{1}{2}$

So in $\Delta ABE$

$\sin B=\frac{AE}{AB}=\frac{1}{2}\angle B={30}^{\circ }$