Question #db197

Aug 9, 2016

$E D = 4$

Explanation:

Here ED will bisect $\angle A D C = {120}^{\circ}$. So $\angle A D E = \frac{1}{2} \angle A D C = \frac{1}{2} \times 120 = {60}^{\circ}$

Again the diagonal of a rhombus bisrcts each perpendicularly.
So in $\Delta E A D \to \angle A E D = \text{Right angle}$

Now $\frac{E D}{A D} = \cos \angle A D E$

$\therefore E D = A D \times \cos {60}^{\circ} = 8 \times \frac{1}{2} = 4$