A rope with its two ends held in place forms a curve called a catenary (assuming that the stiffness of the rope is negligible). A catenary takes the shape of the function:
f(x) = a cosh(x/a),
where cosh is the hyperbolic cosine function.

If a 50-foot rope hangs by its ends from two flagpoles, one 50 feet tall and one 40 feet tall, and at its lowest point is 20 feet above the ground, how far apart are the flagpoles?