5.2.4.17 Various Problems on the Plane

In the triangle \ (a b c \) side \ (a b \) has the length \ (\ sqrt {3} \), height \ (c d \), lowered to the side \ (a b \), the base \ (d \) height \ (c d \) lies on the side \ (a b \), the length of the section \ (a d \) equal to the length of the segment \ (b c \). Find the length of the side \ (a c \).