Find Distance between Poles Given Hanging Cable

[soroban]

The ends of an 80-foot cable are attached to the tops of two 50-foot pole.
The lowest point of the cable is 10 feet from the ground.
Find the distance between the poles.

                L = 80
         *                 *
         |                 |
         |                 |
         |*               *|
         |                 |
      50 | *             * | 50
         |  *           *  |
         |    *       *    |
         |        *        |
         |        :        |
         |        :10      |
         |        :        |
         *--------+--------*
         : - - -  x  - - - :

The equation of a hanging cable is not a parabola.

It is a catenary, with the basic equation: .$$y \:=\:\frac{e^{ax} + e^{-ax}}{2}$$[There is a reason why this problem is not
. . listed under "Challenge Questions".]

 

[kanderson]

This is what I used to get my bridge design lol. I had to write a paper on this. Wish I could find it on my school computer and give it to you guys. Here is a mathematician from oxford that is inspiring and talks about catenary The Catenary - Mathematics All Around Us. - YouTube Although not an explanation more like trying to get people to see something in mathematics, here is one that explains catenary curve The Catenary - YouTube .

 

[Opalg]

I'm thinking, what happens when the poles get closer and closer together? View attachment 716Aha! So that's why you wrote "pole" rather than "poles", I thought it was just a typo.

 

[soroban]

Hello, Opalg!

You got it!

The word "pole" was indeed a typo.
I've corrected it.