A Rope, Two Telephone Poles... and Some Confounding Math

The Puzzler

RAY: I promised a mathematical puzzler this week, so here it is.

TOM: Real numbers-and irrational conclusions, I bet.

RAY: Probably. There are two telephone poles. Each one is 100-feet tall. They are parallel-and an unknown distance apart.

We're going to attach a 150-foot rope from the very top of one of the poles, to the top of the other. This rope will, of course, droop down somewhat.

That drooping rope is called a "catenary," from the Latin word for chain.

TOM: Did they have chains in ancient Rome?

RAY: Of course! The lions were chained to the floor! No, that was the Christians.

So, we've got these two 100-foot poles, and a 150-foot rope. The rope is between the two poles, and it's going to droop down, making an arc.

The question is, what must be the distance between the two poles, so that the lowest point of this catenary is 25-feet above the ground?

Think you know? Drop Ray a note!

[ Car Talk Puzzler ]

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