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?

Question

Zaria Roy

Mathematics

25 March, 17:58

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?

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Kenneth Guerra · Answer 1

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.