## 1st pole 'a' ft tall, 2nd 'b' ft tall, poles 'd' ft apart,

Geometric formulae, word problems, theorems and proofs, etc.
fosteredge
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### 1st pole 'a' ft tall, 2nd 'b' ft tall, poles 'd' ft apart,

Circus tents are held up by poles. For stability, the poles are tied together - the top of one pole is tied to the bottom of the next pole, and vice versa. In between the two tents, the lines cross.

If the first pole is 'a' feet tall and the second pole is 'b' feet tall, and the two poles are 'd' feet apart, at what height do the tie lines cross ?

mathnoob
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Joined: Tue Jul 28, 2009 12:39 pm

### Re: 1st pole 'a' ft tall, 2nd 'b' ft tall, poles 'd' ft apar

I think you can do this by having the one pole based at the origin and the other pole to the right. Then do the line equations for the two supports. Set the line equations equal and solve for "x=". Then plug into one of the line equations to get "y" which is the height.

I get y=(b/d)x, y=a-(a/d)x

fosteredge
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Joined: Mon Sep 06, 2010 6:18 am
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### Re: 1st pole 'a' ft tall, 2nd 'b' ft tall, poles 'd' ft apar

Thanks a lot. It works.