A laundry line, 190 inches in length, hangs between the tops of two poles that are each 135 inches high. The middle of the rope hangs 40 inches above the ground. What is the distance between the two poles?

OK - this may look complicated, but it's not. It's a trick question...

First, think through - you are told the length of the line, and you can calculate how much it sags in the middle. Now, what's the maximum amount a laundry line 190 inches in length could ever sag in the middle? And under what conditions would that occur? Now you should have your answer!

First, is this a homework assignment?

It is not possible to calculate the caternary of the clothes line without knowing the weight of the line, how much tension is on the line, etc. The best you can do is use geometry to approximate the final answer, to any degree of accuracy.

CaptainRich - you would be correct about the catenary, except for the special case that this problem entails. No complicated mathematics needed!