Applied Optimization

Two poles are connected by a wire that is also connected to the ground. The first pole is $11ft$ tall and the second pole is $25ft$ tall. There is a distance of $144ft$ between the two poles. Where should the wire be anchored to the ground to minimize the amount of wire needed?

The wire should be anchored to the ground at a distance of above in order to minimize the length of the wire. feet from the pole labelled $A$ in the diagram

NOTE: Type an exact value in the answer blank.