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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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#1

Re: How do we solve this math problem?

04/28/2007 6:35 PM

Define each ladder as a line in the form y = mx + b. Then solve simultaneously:

The 32' ladder: y = 32/24x + 0 ==> y = 1.333x

The 27' ladder: Need to solve for b (the intercept) b = Sqrt(27^2 - 24^2) = 12.37'

y = -27/24 + 12.37 ==> y = -1.125x + 12.37

Take the first equation and get in terms of x: x = 0.75y

Substitute into the second equation: y = -1.125 (0.75y) +12.37

Solve for y: y = -0.844y + 12.37

1.844y = 12.37

y = 6.71'

Mike

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#5
In reply to #1

Re: How do we solve this math problem?

04/28/2007 10:45 PM

Mikero you are so close but made a crucial mistake! Nice try.

The equations for each line are:

y1 = 0.882 x1

y2 = -0.515 x2 + 12.369

let y1=y2, x1 = x2 , subtract the equations from each other and solve for y to get the height (shown as x on the drawing):

y = 7.81' = X shown on drawing

Why do the equations for each line differ from yours? Because the linear equation should use a slope = rise / run + intercept. You used the length of each ladder for the rise which is incorrect. As you know, you need to calculate the rise using the Pythagorean theorum:

Rise1 = sqrt(32^2-24^2) = 21.166

Rise2 = sqrt(27^2-24^2) = 12.369

The slopes become

S1=21.166/24 = 0.882

S2=-12.369/24=-0.515

which appear in the above linear equations.

J

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#6
In reply to #5

Re: How do we solve this math problem?

04/29/2007 6:14 AM

Yeeks - right you are

Thanks!

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#7
In reply to #5

Re: How do we solve this math problem?

04/29/2007 8:39 PM

Dear Guest,

Thanks to you, and Mike, for getting me on the right track. Makes perfect sense now.

Much obliged,

John

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#22
In reply to #5

Re: How do we solve this math problem?

04/30/2007 3:35 AM

Here is my attempt... 7.8069640... But #20 got a more accurate answer ,
" x=1/(1/a+1/b)=7.80696391893924"

And also in feet and inches 7'-9 87/128

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#77
In reply to #22

Re: How do we solve this math problem?

05/04/2007 11:15 PM

Message to oomsarel:

Could you please explain how you brought a drawing/sketch in the window? I tried several approaches but they did not work and I would like to make a comment with help of a figure.

Thanks in advance Nickname

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#84
In reply to #77

Re: How do we solve this math problem?

05/05/2007 9:01 AM

Hi nick name,

Since nobody has answered your query of how to insert an image here are the instructions.

The Editor tool bar looks like this

If you click on the image button a screen like this will appear.

If you follow the following steps you will be able to insert you image

  1. Click on the image button
  2. Do one of the following
    1. Enter the URL of the image you wish to insert manually
    2. Click the browse button and using the browser select the image you wish to insert from you local machine
  3. If you wish to align the image so that text appears next to it select one of the following. Leaving this blank will configure the image to have text before and after it but not next to it.
    1. Left will align the image with the left margin and allow text to be entered to the right of the image.
    2. Right will align the image with the right margin and allow text to be entered to the left of the image.
  4. Click the Submit button
  5. The text will now appear at the beginning of the post that you are creating you can now do the following.
    1. Drag the image to where you wish it to appear within the post
    2. Resize the image by dragging an edge or corner of the image.
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#86
In reply to #84

Re: How do we solve this math problem?

05/05/2007 12:13 PM

Hi Masu,

Thank you very much I appreciate it.

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#79
In reply to #22

Re: How do we solve this math problem?

05/04/2007 11:31 PM

Hey oomsarel,

Is your avatar a self-portrait?

Regards,

Mike

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#80
In reply to #79

Re: How do we solve this math problem?

05/05/2007 12:24 AM

Mike - Can you explain ILM to a Brit , and the lower part of you image looks like 'custard' (!) . I am intrigued . Kris

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#82
In reply to #80

Re: How do we solve this math problem?

05/05/2007 7:19 AM

Hi Kris,

Sure - ILM is the airport designation for Wilmington, NC and the avatar is the Logo for Taylor Guitars. I've had a nice 410 model for the last 8 or 9 years and it's the finest guitar I've ever owned (and it was one of the cheaper ones)!

Surprised you didn't ask about Thulcandra though.

Cheers!

Mike

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#83
In reply to #82

Re: How do we solve this math problem?

05/05/2007 8:25 AM

Thanks Mike ,

I saw the airport designation on google, but wondered if there was another meaning (I was expecting a state ie Illinois , but couldn't get my head round ILM ). I don't know much about guitars , but a custard one could be interesting - must get my eyes checked !)

Thulcandra I assumed was a real place - I should have known better , living in Etherville

Rock on dude . Kris

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#90
In reply to #83

Re: How do we solve this math problem?

05/05/2007 1:52 PM

Thulcandra IS a real place, but the name isn't

FYI should you be interested...

http://en.wikipedia.org/wiki/Space_Trilogy

Mike

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#93
In reply to #90

Re: How do we solve this math problem?

05/05/2007 9:35 PM

Is this the Sci-Fi book where man goes to Mars and finds all this red foliage all over the place, and there are these slow moving creatures called "Horum" (or something like that)? And eventually they find a stone carving with the spirits of the various planets on it, and on the one representing Earth, the spirit is bound like a prisoner?

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#96
In reply to #93

Re: How do we solve this math problem?

05/05/2007 10:38 PM

That sounds like a Heinlein (sp?) book plot - not the same book.

In "Out of the Silent Planet" (the silent planet is Earth or Thulcandra), Ransom (protagonist - a professor of philology) does go to Mars, kidnapped by the evil Dr. Weston. On reaching Mars, Ransom escapes to be be befriended by the Hrossa and later gets off to the highland, the realm of the Sorn. Multiple adventures ensue. I enjoyed the book.

Mike

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#92
In reply to #80

Re: How do we solve this math problem?

05/05/2007 9:28 PM

First, you have to be careful when talking about food items with a Brit. Custard can mean many things. I think the term goes way beyond what Americans think of as custard.

Second, never order pie in the U.K.. Anything... And I mean anything can be pie as long as it can fit inside a pastry shell. Don't even ask about puddings!!!

"Look, do you have anything with not so much rat in it?!"

"There's the strawberry tart."

"Does that have rat?"

"Well, yes some."

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#99
In reply to #92

Re: How do we solve this math problem?

05/06/2007 1:05 AM

Don't go here vermin !

In America you have peanut butter and 'jelly' sandwiches.Apart from that sounding gross , we call that stuff 'jam' I think. What do you call that which we call 'jam' 'jelly' (apart from it's use in old films for blowing stuff up).

I have to agree , never eat anything called pie (there is a joke here , but it's too rude even for me ). Especially if it's crusty or flaky.

Who would have thought custard was this complicated

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#105
In reply to #99

Re: How do we solve this math problem?

05/06/2007 7:52 PM

Lorries and lift... All that stuff.

I will tell you that while I love the taste of peanuts, I have never been able to eat that foul stuff called "peanut butter!" First, it's not butter and second it tastes absolutely nothing like peanuts. It has all the charm of rancid linseed oil!" So I agree with that one.

On your joke, I have no problem, but woof!!!! You're skating awfully near to the "thought police."

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#108
In reply to #105

Re: How do we solve this math problem?

05/07/2007 2:15 AM

You mean BG ?

I hate all pastry.

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#102
In reply to #92

Re: How do we solve this math problem?

05/06/2007 5:31 AM

Look, do you have anything with not so much rat in it?!"

"There's the strawberry tart."

"Does that have rat?"

"Well, yes some."

What about American beer that's like making love in a canoe!

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#110
In reply to #102

Re: How do we solve this math problem?

05/07/2007 3:17 AM

I agree with you. In fact, I really don't get beer in general. Personally (and I mean just me), it tastes like dirty water and it gives me an instant headache. It's like "hangover potion," without any buzz to enjoy.

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#91
In reply to #79

Re: How do we solve this math problem?

05/05/2007 5:59 PM

Hi Mike. I sent you my answer to your question to your mailbox...

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#95
In reply to #91

Re: How do we solve this math problem?

05/05/2007 9:45 PM

oomsarel, Hey! How's it been going since the "Great Oil Paint Caper?"

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#32
In reply to #5

Re: How do we solve this math problem?

04/30/2007 8:29 AM

Good show! Now I know where to go with my unsolvable math problems! One question, if I may. We teach kids that division by zero is meaningless. Suppose we divide the numerator by ever decreasing values that approach zero. Would the answer be a good approximation? Or would the answer be essentially infinity?

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#39
In reply to #32

Re: How do we solve this math problem?

04/30/2007 10:36 AM

Now this a Calc prof might give you the time of day for. Has a little more to do with what they teach in a Calculus class.

It's something like taking the limit of (whatever/ i ) as i 'goes to' 0+ or 0-

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#41
In reply to #5

Re: How do we solve this math problem?

04/30/2007 11:13 AM

Hi,

I would like to know how this was done, does it with sin and cos ?

Regards

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#76
In reply to #1

Re: How do we solve this math problem?

05/04/2007 7:24 PM

The slope m is not 32/24. You need to use the tangent not the inverse of the cosine. DRB

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#78
In reply to #76

Re: How do we solve this math problem?

05/04/2007 11:26 PM

Dear Guest (why don't you join?)

If you had read all the other posts, you would have seen that my mistake had already been pointed out - and, that I have confessed to the error.

Mike

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#2

Re: How do we solve this math problem?

04/28/2007 7:22 PM

Never mind the maths problem a scale drawing will soon solve that one.

What did the cat see?

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#3
In reply to #2

Re: How do we solve this math problem?

04/28/2007 8:16 PM

Yes, but isn't it always good to be able to work out problems mathematically, hmmm?

Regards,

Mike

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#4
In reply to #3

Re: How do we solve this math problem?

04/28/2007 9:04 PM

Ok but why was his teacher giving him that look? You are of course right but I find maths a mjor problem after a brain injury. So any short cut is useful.

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#37
In reply to #4

Re: How do we solve this math problem?

04/30/2007 10:23 AM

"Ok but why was his teacher giving him that look?"

Because this insn't a Calculas question. This is more highschool trig and alg.

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#8

Re: How do we solve this math problem?

04/29/2007 10:59 PM

have you forgotten how to measure the height of a triangle??????????????????

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#9

Re: How do we solve this math problem?

04/29/2007 11:05 PM

Your teacher was being sarcastic, surely.

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#10

Re: How do we solve this math problem?

04/29/2007 11:07 PM

John: It is Algebra that you need here with some knowledge of Geometry. Using Pythagoras theorem, we can determine the lengths of the triangle that you defined with the ladders. C1 on the left will be the Squareroot of 27 * 27 - 24 * 24. Similarly, C2 on the right will be the Squareroot fo 32 * 32 - 24 * 24. The value that you want to measure as X is nothing but (C1 * C2) / (C1 + C2) {using proportions - the algebra part}. If you do the math, you will get C1 = 12.4, C2 = 21.2, X = 7.8.

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#13
In reply to #10

Re: How do we solve this math problem?

04/29/2007 11:39 PM

I thought that only worked on right triangles?

Which these don't appear to be

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#14
In reply to #13

Re: How do we solve this math problem?

04/29/2007 11:45 PM

Garth: Ofcourse, there are right triangles. Follow the triangle defined by the lengths 27' and 24'. C1 is the other side of the right triangle.

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#11

Re: How do we solve this math problem?

04/29/2007 11:27 PM

may be the answer is 0.346'.

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#12

Re: How do we solve this math problem?

04/29/2007 11:35 PM

I'm with BrainWave, there are several ways to solve this problem, The important question is what happened to the cat to get that reaction and the corollary will it work on teenagers?

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#15

Re: How do we solve this math problem?

04/30/2007 12:56 AM

I remember this problem given to us by my teacher in Math class back in 1948 at (RIT), Rochester Institute of technology. The class was unable to solve it but a friend of mine came up with the correct answer using a system called determinants. This suprised the teacher.

I never did understand how he did it. Anyway this problem is as old as the hills and so am I at age 80.

There must be somebody out there that would know about this system.

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#30
In reply to #15

Re: How do we solve this math problem?

04/30/2007 7:25 AM

Being nearly of that generation, I'd have been surprised too - that most of the class couldn't solve it. Once you have the heights at the ends of the ladders, (Pythagorus), you just use that the size ratios in 'similar' figures are equal for the relationships between the horizontal distances, to create some very simple algebra that leads to the result presented by Babu. Determinants are really overblown for solving such simple simultaneous equations, so I would have been surprised and unimpressed in approximately equal measure at their use in this case. All the other stuff was the bread-and-butter of the high-school maths syllabus in the years before 1948 - but maybe the war interfered with the teaching.

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#33
In reply to #15

Re: How do we solve this math problem?

04/30/2007 8:31 AM

The theory is called Cramer's Rule. Many ways to explain it, here I picked one from wikipedia.

The system of equations is represented in matrix multiplication form as:

where the square matrix A is invertible and the vector x is the column vector of the variables: (xi).

The theorem then states that:

where Ai is the matrix formed by replacing the ith column of A by the column vector c.

A good way to use Cramer's rule on a 2×2 matrix is to use this formula:

Given

and,

which in matrix format is

x and y can be found with Cramer's rule as:

and

Our two lines can be formulated by:

m1x + y = c1 with m1 = -sqrt(322 - 242) / 24 and c1=0

m2x + y = c2 with m2 = sqrt(272 - 242) / 24 and c2=sqrt(272 - 242)

Using Cramer's Rule and solving for y :

y = (m1c2 - m2c1) / (m1 - m2)

substituting the known value ones will arrive to y = 7.81" as found with other ways.

"The candle will not shine the night sky, but the ray will go everywhere in straight path."

Only my fault was to make it biased.

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#16

Re: How do we solve this math problem?

04/30/2007 1:00 AM

Just for starters, you said they were "equal length" ladders, then you show one as 27 feet and the other as 32 feet. What's up with that?!

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#17
In reply to #16

Re: How do we solve this math problem?

04/30/2007 2:35 AM

Actually he did said, "Given that 2 unequal length ladders.."

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#51
In reply to #17

Re: How do we solve this math problem?

04/30/2007 3:05 PM

Well, I guess that proves: If you drink don't CR4. If you CR4, don't drink!

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#59
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Re: How do we solve this math problem?

04/30/2007 11:52 PM

You crack me up vermin ! Ace . Now I know why your Avatar hasn't shaved ROFLHO. That would be good for a thread - 'things you shouldnt do while cr4-ing/times you shouldn't be cr4-ing' . I'm keeping quiet about mine (the wife thinks I'm only having cyber-sex).

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#61
In reply to #59

Re: How do we solve this math problem?

05/01/2007 1:31 AM

I calls them as I sees them... or at least as I think I sees them.

Besides, if I shaved, I'd be naked.

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#62
In reply to #61

Re: How do we solve this math problem?

05/01/2007 1:59 AM

I might get pickled so I can see 2 of you . Double the fun . Please God -don't shave. Unless you're babalicious.

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#94
In reply to #59

Re: How do we solve this math problem?

05/05/2007 9:40 PM

I had a bikini wax one time... I couldn't open my eyes for a week!

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#100
In reply to #94

Re: How do we solve this math problem?

05/06/2007 1:08 AM

I knew you got your pic from somewhere. An all in one job eh - nice souvenir.

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#18

Re: How do we solve this math problem?

04/30/2007 2:58 AM

Hi johnjohn,

This is a very simple math problem.

First, apply Pythagorean Theorem to find the elevations of the top of the 2 ladders. The shorter ladder to be 12.37 ft and the longer ladder to be 21.17 ft. respectively.

Second, since you already computed the corresponding elevation, using basic trigonometric functions you can now find the angles of inclination of the ladders. The shorter to be 27.27 degrees and the longer to be 41.41 degrees respectively.

Third, the sum of the interior angles of any triangle, as we know it, to be 180 degrees so the angle at which the 2 ladders intersect where the distance x is to be calculated is 180-27.27-41.41=111.32 degrees.

Fourth, since we have already computed the 3 interior angles of that triangle and with 1 given side, we can now compute for the bottom segments of the ladders using Sine Law. These segments form part of the triangle for computing x. Please note that the shorter segment thus form is from the longer ladder and the longer segment thus form is from the shorter ladder. Applying Sine Law will give the shorter segment value of 11.80 ft.while the longer segment value of 17.04 ft..

Finally, we can now compute for x using the trigonometric sine function of the right triangles thus form by a vertical line that defines x. The value of which is 7.81 feet.

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#29
In reply to #18

Re: How do we solve this math problem?

04/30/2007 6:03 AM

Still something is missing, which I could not figure out. How the segment is measured when 24 ft radius circle do not touch any right angle ; neither 27 ft ladder nor 32 ft ladder do not show any base angles of the ladders?

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#19

Re: How do we solve this math problem?

04/30/2007 3:22 AM

If you use trigonometry and a little bit euclidean geometry it is easy

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#20

Re: How do we solve this math problem?

04/30/2007 3:27 AM

Be

a=sqrt(272-242)=12.3693 b=sqrt(322-242)=21.1660

then (applying Thales Theorem for the two triangles)

x=1/(1/a+1/b)=7.80696391893924 (harmonic average).

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#21

Re: How do we solve this math problem?

04/30/2007 3:34 AM

Very good question but to test the mathematicians amongst us try 2 ladders of 24 and 30ft cross at 10 ft in a similar arrangement. How wide is the alley? Looks simple but is it? (Answers to 5 dec places excludes drawing)

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#23
In reply to #21

Re: How do we solve this math problem?

04/30/2007 4:39 AM

Yes simple enough . The width of the alley is 17.11119 feet. How is that?

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#64
In reply to #21

Re: How do we solve this math problem?

05/01/2007 4:12 AM

Hi AndyH

I do not understand where is the problem, your question is as simple to solve as the other. Let us note L1 and L2 the 2 ladders length and h the Height of the crossing point. Let us also define the distance between the walls as Lo. If you consider the functions A1= (L1^2-Lo^2)^0.5 and A2=(L2^2-Lo^2)^0.5 you come to an equation where Lo,L1,L2 and h are connected to eachother: E(Lo)=A1*(1/h-1/A2)-1=0

This equation can be solved by iterration using the tangent method:

Lo(i)=Lo(i-1)-E(Lo(i))/E'(Lo(i)) where E' is dE/dLo. Of course a seed is requested for such an approach.

For such function the convergency is very rapid and for the dimensions you gave as

L1=24;L2=30 and h=10 the result is Lo=

17.852914 after only 6 steps.

The programm could also be written in relarive dimensions and thus valid for any other combination if for instance you take L2 as reference and write in place of L2 1 and in place of L1 the ratio L1/L2 and of course in stead of h the ratio h/L2. The result will be the ratio Lo/L2.

The computation was made with EXCEL so that the accuracy is quite good.

I hope to have answered to your question.

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#112
In reply to #21

Re: How do we solve this math problem?

05/11/2007 8:12 AM

AndyH, Very perplexing. I am not a mathematician and could not understand either of the replies to your query. I have been trying to solve this problem with no success. Can you explain the process to someone whose last math course was Trig/Solid in high school. I'm a little rusty that was 40 years ago. I do work with tri daily but do not consider myself great at math.

If you have the time and the ability I would be appreciative.

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#24

Re: How do we solve this math problem?

04/30/2007 4:57 AM

dear Johnjohn,

We have a complete solution to this proble as well it is quite long. Contact on my email id syngloss@gmail.com. We have solved similar questons earlier also but disclose your identity.

Regards

Arun Ralhan

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#25

Re: How do we solve this math problem?

04/30/2007 5:13 AM

I'm afraid it was disbelief, not sarcasm; and, as you have seen, calculus is unnecessary. I'm told high-school maths have gone downhill; even so, this continues to be set as an exercise for 15-16 year-olds in the UK

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#26

Re: How do we solve this math problem?

04/30/2007 5:16 AM

For general amusement , go to this link and click on find for a nice problem.

http://agutie.homestead.com/FiLEs/LangleyProblem.html

The solution is great. Have fun.

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#27
In reply to #26

Re: How do we solve this math problem?

04/30/2007 5:21 AM

I just ran the animation , and it's actually more fun on a scap of paper

The point is , that you find the missing angle without Trig or calculus by adding to the construction. Nest time I'll draw and scan the darn thing.

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#28

Re: How do we solve this math problem?

04/30/2007 5:53 AM

Johnjohn, Please draw a circle with radius 24 ft. If circle touches at the end of 21.16 ft, i.e., (Sq.32 minus square 24) you can measure, Here the circle do not touch, as such the length can be measured with a scale practically. Same way if circle with a radius of 12.37 (ht of left vertical line) touches the chord, it can also be measured. Here also you can not make the circle touch at any two point of the squares. Hence,

Plain answer is you are 46 years old (my neighbour is only 23).

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#31

Re: How do we solve this math problem?

04/30/2007 7:34 AM

x=7.807. You build up an equation x=a*tan(acos(24/32))=(24-a)*tan(acos(24/27)).

The result is "a" and x= a*tan(acos(24/32)). It is often so that one find himself bolcked on a problem. I had myself such a situation many years ago.

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#34

Re: How do we solve this math problem?

04/30/2007 8:53 AM

This is very basic common sense problem

Calculate the angles using basic trig

then reverse the formula to calculate the height of x

y=mx+b to determine intercept will also work.

duh!

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#35

Re: How do we solve this math problem?

04/30/2007 9:13 AM

But let us complicate the problem:

imagine the indicated sloped lenghts refer to distance between the walls and the intersection.

Now the problem will be a little more complicate.

How to solve, then?

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#36

Re: How do we solve this math problem?

04/30/2007 10:15 AM

the 2 triangles are supposed to be rectangle, there are different ways to get the solution. On my opinion the simplier is :

cal the cross point of 32' and 27' lines M.

Clockwise from bottom left corner call the point of the left triangle (with longer side 27') A, B, C.

The right triangle (with longer side 32') points are A, D, C.

Put a point E, straight below M on the segment AC (ME is perpendicular to AC).

Now triangles ABC and EMC are similar, so are similar ADC and AME.

Call length of ED unknown variable Y.

You can state that for the lengths of each segment :

X / Y = AB / AC [ AC = 24 AB = square root (27^2 - 24^2) ]

X / AE = DC / AC [ AE = 24 - Y DC = square root (32^2 - 24^2) ]

this a system of 2 variables on 2 equations and it is totally determined.

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#38

Re: How do we solve this math problem?

04/30/2007 10:23 AM

How do we solve this math problem? - "with knowledge and brain - "

x=[(√153*√448)/(√153+√448)]

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#45
In reply to #38

Re: How do we solve this math problem?

04/30/2007 11:34 AM

x=[(√153*√448)/(√153+√448)]

x=[(AB)/(A+B)], A=√153, B=√448

x=[(AB/(A+B)][(A-B)/(A-B)]

x=[(A2B-AB2)/(A2-B2)]

x=[(153√448 - 448√153)/ (153-448)]

x= - [(153√448 - 448√153)/ 295]

It's been a while, but I think that's correct.

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#56
In reply to #45

Re: How do we solve this math problem?

04/30/2007 8:02 PM

No comments.

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#55
In reply to #38

Re: How do we solve this math problem?

04/30/2007 7:59 PM

I supose you are not kidding.

If this is the solution, so my congratulations.

Regards

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#70
In reply to #38

Re: How do we solve this math problem?

05/02/2007 2:12 AM

Pitagoras + Ruler 3:

x = √(272 - 242) = √153

y = √(322 - 242) = √448

m + n = 24

z = [xn/24] = [y(24 - n)/24]

xn = 24y - yn

n = 24y/(x + y)

z = [xn/24] = [x*y / (x + y)] = [(√153*√448) / (√153 + √448)]

z = 7.806963918939240 (Lqqd)

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#71
In reply to #70

Re: How do we solve this math problem?

05/02/2007 2:50 AM

Upss.... change the letters.

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#40

Re: How do we solve this math problem?

04/30/2007 11:11 AM

I think he was being sarcastic :)

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#42

Re: How do we solve this math problem?

04/30/2007 11:13 AM

i just counted the squares.. got 8 ft and it only took 10 sec. not much help sorry :) although it did take much longer to type this response. i guess it depends on how accurate you need to be or if it is just a technical exercise..

rick

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#43

Re: How do we solve this math problem?

04/30/2007 11:13 AM

You could also make a scale drawing and then measure "x". It would be close enough for ladders.

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#44

Re: How do we solve this math problem?

04/30/2007 11:29 AM

First, as others noted this is not a Calculus problem. If you are asking you old calculus professor professor this you make him think' "Why did I pass this guy?"

Second, these types of problems always raise more questions in my mind.

How thick was the ladder? It can not be zero as your sketch suggest.

Were both buildings perfectly flat? Most building have some overhang at the foundation.

Were both building perfectly normal to the ground and the ground perfectly flat?

Does the ladder have a swivel foot and what is the location of the axis of rotation? Most do.

What does the top of the ladder look like? Does either have a spreader bar for stability?

Are these extension ladders with on ladder offset sliding over the other? Which way is the offset in each? 32' ladders are mostly all extension ladders.

And what is the spacings of the rungs and the distance from the catch mechanism for the parallel / extension ladder. so you can figure the thickness at the point of crossing which you need for the next question.

Is dimension to the bottom of the ladders crossing or the top? What about the case where the extended ladder lower end is at the point of crossing?

More questions than answers

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#46
In reply to #44

Re: How do we solve this math problem?

04/30/2007 11:37 AM

Darn, when I solved I assumed I could model the ladders as perfectly rigid beams. Actually there would be some deflection...

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#47

Re: How do we solve this math problem?

04/30/2007 12:12 PM

Allow me to fan the flames . How can Billy-no-brains trisect any of the angles shown without using any of the methods discussed ? No trig , no pythagoras , no determinents , in fact he doesn't even have to write anything down. Will tell all tommorow unless somebody spills the beans first.

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#60
In reply to #47

Re: How do we solve this math problem?

04/30/2007 11:58 PM
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#48

Re: How do we solve this math problem?

04/30/2007 1:55 PM

I cheated and drew it with a CAD program and it gave 7.8069 feet.

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#49

Re: How do we solve this math problem?

04/30/2007 1:58 PM

Personally, I would just drop a tape measure from the intersection to the ground, but i'm the kind of engineer that wears safety shoes... I remember in my first high school physics class the test was to use a barometer to determine the height of the building.

I said that I would time its fall from dropping from the top of the building ....got an A and a "Science is not always about finding the one right answer " note from my teacher.


He was retired USAF and experienced with dropping things from high places...

milo

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#50
In reply to #49

Re: How do we solve this math problem?

04/30/2007 2:54 PM

If we had the barometer then we could use the same method to find the intersection height! knowing gravity acts at 9.81m/s/s, if we drop the barometer how long would it take to hit the deck, making the asumption that wind resistance and an accurate method of timing are used?

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#58
In reply to #50

Re: How do we solve this math problem?

04/30/2007 9:26 PM

I like practical solutions. I would just take a tape measure and measure from the ladder crossing to the ground.

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#67
In reply to #58

Re: How do we solve this math problem?

05/01/2007 12:44 PM

Me too . I'd also suggest he/she move into the 21st Century and go metric - it would save a lot of time and confusion.

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#65
In reply to #50

Re: How do we solve this math problem?

05/01/2007 10:12 AM

A man after my own heart! I put together this thread to suggest various pragmatic solutions to problems of this type. You'll recognize several CR4 respondent types (including one nut case who goes off on a remarkably unrelated tangent).

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#66
In reply to #49

Re: How do we solve this math problem?

05/01/2007 10:38 AM

There is a much nicer answer to this question by Niels Bohr. I let you have the surprise after finding it.

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#68
In reply to #66

Re: How do we solve this math problem?

05/01/2007 2:39 PM

I've heard the barometer story attributed to Niels Bohr, but I think it was, in fact, written by Alexander Calandra. The first link below has a few good additions to the original story.

http://www.everything2.com/index.pl?node_id=767139

http://www.snopes.com/college/exam/barometer.asp

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#52

Re: How do we solve this math problem?

04/30/2007 4:02 PM

eight feet. Simple, 15 is equal to 24 ft . 5 is equal to X. 24 times 5 = 120 . Divide by 15 = 8

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#53

Re: How do we solve this math problem?

04/30/2007 4:41 PM

Okay guys I get the message!

It's true, I should have thought this one through a little more. Regarding post #15, I know this problem is old as the hills (almost as old as me). I first ran into it back in the fifties. But I have to fall back on the situation that post #31 (NICK NAME) gave- it's just one of those that I had a mental block about.

To posts #25, 37, an 44, I never implied that this was a calculus problem. Only that I asked the question of my calculus professor. Incidentally, to #44, I did quite well in that class, thank you.

Anyway, for what it's worth, the question did apparently generate quite a bit of interest.

Thanks to all,

John

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#54
In reply to #53

Re: How do we solve this math problem?

04/30/2007 5:48 PM

Addendum to post #53,

I should have asked the question of my philosophy professor and then it would have required a philosophical solution. But then just maybe... hmmmm

John

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#57

Re: How do we solve this math problem?

04/30/2007 9:13 PM

8ft 9.56in assuming no gravity but this is asking for an alley which means that there is gravity pressure on the these ladders. which will make the ladders bowing down ward. then not knowing these ladders design then their flexing is unknown. emailing at ma-pa-bexar@tds.net for Hawk

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#63

Re: How do we solve this math problem?

05/01/2007 2:36 AM

I took additional maths as an O level subject in 1955 and we were solving this sort of problem back then. So much for the modern O level syllabus.

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#69

Re: How do we solve this math problem?

05/01/2007 11:44 PM

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,

Hello Johnjohn,

First of all, I don't think your instructor had a clue. I'm not a calculus instructor, but in the world of aerospace, I've had similar problems to deal with in engineer design drawings. It's been twenty years since I've seen anything like this. I don't know how critical this dimension is to you, or what project you have on the board. I would take a more simple route and build this graph to scale. As per example: On the graph paper you are using, use eight, or twelve squares as one foot. Once this is done, then take measurements. I'm sure you'll find your answer. The larger the scale the more acurate is your measurement.

Good luck.

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#72
In reply to #69

Re: How do we solve this math problem?

05/02/2007 1:14 PM

Thanks Guest,

I really appreciate your input. Accuracy was never an issue. I just wanted the different methods for solving this type of problem. As you can see if you read my posts #53 and #54, I never implied this to be a calculus problem. As you, and other CR4 posters, have indicated, drawing the problem graphically, then measuring for the unknown works just fine. I'm pleasantly surprised at the response and interest that this question generated.

Many thanks to you for your practical insights, as well as to all the CR4 folks.

John

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#73
In reply to #72

Re: How do we solve this math problem?

05/02/2007 1:33 PM

Dear Johnjohn

I think that my suggestion was much more intriigating to the others.

I have received a lot of stupid answers as well as lots of uncompatible answers.

Actually, if you consider the indicated slopes to be the part between each wall and the intersection point, it would be very complicate, as the answer could vary from 0 to 32'.

Kind regards

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#74
In reply to #73

Re: How do we solve this math problem?

05/02/2007 1:45 PM

Thanks,

John

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#81
In reply to #72

Re: How do we solve this math problem?

05/05/2007 12:38 AM

Johnjohn, I think you can see by all the postings that the problem wasn't as trivial as you thought it was. By the way, the correct answer is slip your math teacher a $50.00 (teachers don't make much) and bribe him for the answer.

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#85
In reply to #81

Re: How do we solve this math problem?

05/05/2007 10:41 AM

Thanks Vermin,

I don't know much, but I know what I know (usually).

John

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#87
In reply to #81

Re: How do we solve this math problem?

05/05/2007 12:24 PM

How do you define a trivial problem? 2+2=?

My definition is: a trivial problem is a problem which can be solved with usually available knowledge without help of special books or other supports. It is not a shame not to find the solution of a trivial problem. The way our brains work leads to such situations where we block on a theme and are not able to find the solution and another looks 30" and gives the solution. The ladder problem is NOT a complicated problem. There are so many solutions suggested or proposed because there are many ways to attack and solve a problem. The fact that many participated with different solutions is a sign of diversity and fantasy but not a sign of difficulty. It shows how different we are and this is positive for such a discussion field whichever the object or idea we discuss, analyse or develop.

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