3. In a convex pentagon $A B C D E \angle A=60^{\circ}$, and the other angles are equal to each other. It is known that $A B=6, C D=4, E A=7$. Find the distance from point $A$ to line $C D$.
Solution. It is clear that all other angles are 120 degrees, so $A B \| D E$ and $B C \| A E$. Also, $D E=2$ and $B C=3$. The desired distance is the height of an equilateral triangle with side 9 (to which the original pentagon can be completed), which is $\frac{9 \sqrt{3}}{2}$.