A not quite as tough as jothaxe's problem problem

[thEnEuRoMancER]

The alley is 4.0123 ft wide (rounded to 4 decimals).
The answer was obtained numerically.

 

[Jothaxe]

Before I was solving the equations by hand and I hoped it came out to 4' exactly.

Now after solving the equations numerically on my calculator, I get:

w = 4.0123112 feet wide.

I think this is correct. Can anyone verify?

-jothaxe

 

[GasX]

There is a reason I can't prove it... :frown:

 

[Jothaxe]

<< The alley is 4.0123 ft wide (rounded to 4 decimals).
The answer was obtained numerically. >>



I guess that pretty much verifies things then!

Nice!

-jothaxe

 

[palad]

I see what you're saying, I was thinking in 2 dimensions and wondering how you could get two ladders to intersect in an x without some creative cutting. Now I understand you're talking about the ladders leaning against opposite walls.

 

[Jothaxe]

Quaggoth:

You mentioned that you want to know how to solve the problem. The basic idea is to recognize the similar triangles and get some equations this way. Then use the right triangles at the bottom to get more equations. Then combine all these equations to reduce to just one variable and solve for it (numerically.)

Here is my diagram, and a rough outline of the necessary analysis.

Its too hard to do math here so I just scanned it in.

-jothaxe

 

[Quaggoth]

OK, you are all nutz (Or I am).

The alley is, I believe 8' wide.

we have to assume that the alley is level. The plumbline hangs straight down (Gravity will do this). since the plumbline (One side) is 3', and the triangel should be a right triangle, a2+b2=c2 that would be 9+16=25. The plumbline side is 3', the alley floor side is 4', and it's 5' from where the ladder butts against the wall to the intersection (The hypotenuse).

OK, I think I am wrong, because the plumbline wouldn't be in the center unless we have 2 ladders of = length. Damn, I'm nutz.

 

[Quaggoth]

Hmm, too late on my last post.

Jothaxe, that seems to look right. I guess my best guess answer of 8' was a ways off. Thanks for the answer jothaxe and thEnEuRoMancER. Anyone have any more problems?

 

[Jothaxe]

<< Anyone have any more problems? >>



Sure thing. Let me post it in another thread though...

-jothaxe