A fence 6 feet tall runs parallel to a tall building at a distance of 5 feet from the building. what is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?

Generally a 45 degree angle is the best angle. this yields the smallest triangle with a 6' fence vertical side. As the ladder reaches the wall, two similar triangles are resolved. the 45 degree angle that the ladder makes with the ground yields a 6x6 legged right triangle. Adding 5' to the ground makes the larger 45 degree triangle with a base of 5+6=11' side. Using the formula for Special Triangles, 45-45-90 gives the ladder a 11 times the Squareroot of 2 for its length.