A fence 6 feet tall runs parallel to a tall building at a distance of 5 feet from the building. What is the le

Question

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?

Answer 1

The shortest distance would be a ladder at a 45 degree angle, covering the 5 feet outside and 6 feet inside - 11 feet and the hypotenuse would be (11^2 + 11^2 )^0.5

((11^2) + (11^2))^0.5 = 15.5563492

just under 15' 7"

Answer 2

Let:

A = the angle the ladder makes with the ground

L = length of the ladder

L = 6/sinA + 5/cosA

dL/dA = -6cos/sin^2A + 5sinA/cos^2A = 0

-6cos^3A + 5sin^3A = 0

sinA/cosA = tanA = (6/5)^(1/3) = 1.06266

A = 46.73997 degrees

6/sinA = 8.23892

5/cos A = 7.29596

L = 8.23892 + 7.29596 = 15.53488 FT

Answer 3

length of ladder = (6/sin(x))+(5/cos(x))

angle x at 46.75 gives ladder length 15.53489189 feet