2 poles 20' high x apart with a rope 30' long 5' off ground. What is formula for solving for X?

Question

rope is attached to each pole hanging in a arc 5" off the ground.

it is 5 feet not inches

Answer 1

A rope hanging from poles follows a catenary curve, y=a*cosh(x/a) where a is the distance from the bottom of the curve to the x-axis.

In the case you have given, a = 5ft. To find the distance between the poles, this is 2x' where x' is the value of x when y = 20ft. This gives the formula

20 = 5*cosh(x'/5)

cosh(x'/5) = 4

x' = 5*arccosh(4)

x'= 10.317ft, so the distance between the poles is 20.63ft