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Johnjohn
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How do we solve this math problem?

04/28/2007 5:09 PM

Hello friends,

Given that 2 unequal length ladders span an alleyway as shown in diagram, how do we find dimension X? I have puzzled over this one, off and on, for years and have not been able to solve it. I once asked my old calculus professor about it and he just sat and stared at me. I don't know if he was just being sarcastic or if he just didn't want to answer the question

Thanks,

johnjohn

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Johnjohn
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#88
In reply to #87
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Re: How do we solve this math problem?

05/05/2007 12:45 PM

Hi NICK NAME,

Vermin is corect. It is obviously not a trivial problem.

Wiktionary: trivial (math); 1. an equation in which every variable is equal to zero. 2. self-evident.

This problem does not fit either case so it is not trivial.

2+2=? (is that 2.0000000 + 2.0000000 =? or is it 2.0000000 + 2.00000001... =?)?

John

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nick name
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#89
In reply to #88

Re: How do we solve this math problem?

05/05/2007 12:48 PM

OK according to the dictionnary. I am not stubborn. It is true words have their value and for communication we should accept always the same definition.
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#75

Re: How do we solve this math problem?

05/04/2007 7:22 PM

The solution is relatively (please excuse the use of this Einstein word) easy. Instead of using the x value as shown, I am replacing this x with y for simplicity of explanation when using with linear graphs.

The height that the 27' ladder reaches on the left wall comes from Pythagoras Theorem and is equal to

√(272 - 242) = 12.369 (3dp)

The tangent of the angle made by the 27' ladder with the ground is 12.369/24 = 0.515 (3 dp)

Similarly the height that the 32' ladder reaches on the right wall comes from Pythagoras Theorem and is equal to

√(322 - 242) = 21.166 (3dp)

The tangent of the angle r made by the 32' ladder with the ground is 21.166/24 = 0.882 (3dp)

If you then take the origin for a graph to be the bottom where the 32' ladder touches the ground then the two ladders are two straight line graphs.

For the 32' ladder (y=mx+C) and C = 0 as it goes though the origin and the slope m is the tangent which is to 0.882 (from above). Therefore the equation of line for this ladder is y = 0.882x

Similarly for the 27' ladder (y=mx+C) and C =12.369 (as this cuts the y axis the left wall at that value for y) and the slope m is the tangent which is to 0.515 (from above). However, m is –ve therefore m = -0.515 Therefore the equation of line for this ladder is y = -0.515x + 12.369

The two lines (ladders) intersect and therefore the y and x values with be equal at that intersection. Therefore y = 0.882x = -0.515x + 12.369. Therefore 1.397x = 12.369 and x = 8.854 (3dp) and y = 7.809 (3dp).

As this y value is your x then your x = 7.809'

I hope that this solution is of interest. DRB
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Mikerho
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#97

Re: How do we solve this math problem?

05/05/2007 10:51 PM

Everyone,

Isn't it kind of comical that we are now using this thread as a sort of general messaging forum? What stared out as a simple question has now generated an amount of dialogue (Brit sp.!) inconsistent with what the original post (maybe) should have generated, much of it not related to the original topic.

I joined CR4 to try and increase my knowlege of technical things and to help in the rare occasions when I can. To that end, this is working!

Johnjohn, thanks for starting this post - it has been most interesting.

Mike

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vermin
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#98
In reply to #97

Re: How do we solve this math problem?

05/05/2007 11:09 PM

Sooner or later this is how most of these threads go. "I don't want to spank the super-model, but sometimes they're naughty."

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Kris
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#101
In reply to #97

Re: How do we solve this math problem?

05/06/2007 1:14 AM

When a thread weaves on and off topic , that's where you can discover some of the really good stuff. If you want general knowledge , don't just go by a threads title. There are some gems of 'fact' (and humour) about. Use the search button and you'll be amazed where you can end up. From basic maths to well explained complex engineering.

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masu
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#103
In reply to #97

Re: How do we solve this math problem?

05/06/2007 5:59 AM

"Isn't it kind of comical that we are now using this thread as a sort of general messaging forum? "

Yep, it's pretty much what happens whenever you stick a bunch of engineers in a room and add copious quantities of beer!

By the end of the night nobody can remember or gives a stuff, what we were talking about to start with and everybody is talking a strange language that is the verbal equivalent of combination of hieroglyphics and left handed brail.

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Kris
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#104
In reply to #103

Re: How do we solve this math problem?

05/06/2007 8:28 AM

One part of the problem is solved.

Hang on a minute , vermin won't see that

vermin you're a **%$"£& *(**(,& * &()****ing &$**8ed.

Sorry vermin , couldn't resist.

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vermin
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#106
In reply to #104

Re: How do we solve this math problem?

05/06/2007 7:56 PM

Why thank you! That's what we vermin live for! Otherwise, we wouldn't be vermin, now would we.

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Mikerho
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#107
In reply to #103

Re: How do we solve this math problem?

05/06/2007 9:11 PM

And we all end up looking like your avatar in the morning

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Kris
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#109
In reply to #107

Re: How do we solve this math problem?

05/07/2007 2:19 AM

Masu's eyes have Engineered symetry.

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masu
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#111
In reply to #109

Re: How do we solve this math problem?

05/08/2007 9:55 AM

Masu's eyes have Engineered symetry.

You noticed. That mirror copy button on the CAD program comes in really handy some times.

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