Question

b. In a rhombus ABCD, length of each side is 10 cm and angle A is 60°. Find the length
of its diagonal AC. (V3 = 1.73)​

Answer 1

The length of the diagonal $AC$ is $10\sqrt{3}\ cm$

Step-by-step explanation:

Given,

$ABCD$ rhombus where length of each sides $10\ cm$ and $\angle A=60\ degree$

We know,

A rhombus is a parallelogram whose diagonals are perpendicular to each other also the diagonals are perpendicular to and bisect each other. Adjacent angles are supplementary.

∴ $\angle BAO=\frac{60}{2}=30\ degree$

And $\angle AOB=90\ degree$

From $\triangle AOB$,

$cos\angle BAO=\frac{AO}{AB}$

⇒$cos30=\frac{AO}{10}$

⇒$AO=10\times \frac{\sqrt{3} }{2}$

⇒$AO=5\sqrt{3}$

∴ $AC=2AO=2\times 5\sqrt{3}=10\sqrt{3}\ cm$

So, The length of the diagonal $AC$ is $10\sqrt{3}\ cm$