Question

In triangle $ABC$, $BC = 20 \sqrt{3}$ and $\angle C = 30^\circ$. Let the perpendicular bisector of $BC$ intersect $BC$ and $AC$ at $D$ and $E$, respectively. Find the length of $DE$.

Answer 1

DE=10

Explanation:

Given that in triangle ABC, $BC = 20 \sqrt{3}$ and $\angle C = 30^\circ$. Let the perpendicular bisector of $BC$ intersect $BC$ and $AC$ at $D$ and $E$,

To find length of DE

Please refer to the attachment for solution

Since perpendicular bisector we have DC = 1/2 BC = 10 sqrt 3

Using right triangle CDE, we get DE = 10