Question

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

Answer 1

$sin{30}^0=\left(\frac{b}{8}\right)or\left(\frac{1}{2}\right)=\left(\frac{b}{8}\right)\therefore b=4$
$\therefore diagonallength=2b=8cm$
$sin{60}^0=\left(\frac{9}{8}\right)or\left(\frac{\sqrt{3}}{2}\right)=\left(\frac{a}{8}\right)\therefore a=4\sqrt{3}$
$thendiagonallength=2a=8\sqrt{3}cm$