Math Is Fun Forum

bhow

Member

Registered: 2009-10-11

Posts: 2

DESPERATELY URGENT HELP NEEDED FOR THIS SOLUTION. answer in half hr.

DESPERATE URGENT HELP NEEDED. PLEASE HELP WITH SOLUTION for this problem.

There is a 1 m cube wooden box placed up against a wall. A ladder measuring 4 m long is placed so it rests on the floor, touches the edge of the box and the top of it rests on the wall. How far up the wall is the top of the ladder?

Please find solution. Thanks.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: DESPERATELY URGENT HELP NEEDED FOR THIS SOLUTION. answer in half hr.

Hi;

That is not exactly right the base of the triangle formed by the ladder and the wall is not 1m. That is the side of the cube. The base is > 1.

Look here to see what I mean.

http://www.stirlingsouth.com/richard/trig9.htm

Last edited by bobbym (2009-10-11 20:34:51)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

bhow

Member

Registered: 2009-10-11

Posts: 2

Re: DESPERATELY URGENT HELP NEEDED FOR THIS SOLUTION. answer in half hr.

Hi, thanks for the posts. Sadly, the first proposed solution doesn't appear to be correct. Tony, your posts did not give mea solution although I really appreciate the lovely CAD diagram. Would you or anyone else out there happen to have the solution? I would really like to know how to solve this seeamingly simple problem that has vexed me no end.

Cheers.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: DESPERATELY URGENT HELP NEEDED FOR THIS SOLUTION. answer in half hr.

Hi bhow;

Who is Tony? The link was just meant to show that the solution offered might not be correct.

Last edited by bobbym (2009-10-14 18:33:03)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Nook

Member

Registered: 2009-10-14

Posts: 1

Re: DESPERATELY URGENT HELP NEEDED FOR THIS SOLUTION. answer in half hr.

Is there even one real answer? :S

If we assume the height of the wall at which the ladder touches is y and the space between the base of the ladder and the end of the box is x, we could do the following.

So y would depend on what angle the ladder is placed against the wall, which would determine the value of x. I can't say that is right, just a guess.

Last edited by Nook (2009-10-14 18:32:45)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: DESPERATELY URGENT HELP NEEDED FOR THIS SOLUTION. answer in half hr.

Hi;

The ladder is:

1.36219999266324453 m  up the wall

3.760905629544160105 m  from the wall

This forms a right triangle that just touches the cube.

1.36219999266324453^2 + 3.7609056329544160105^2 ≈ 16 = 4^2 m

Last edited by bobbym (2009-10-15 07:45:28)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Fruityloop

Member

Registered: 2009-05-18

Posts: 143

Re: DESPERATELY URGENT HELP NEEDED FOR THIS SOLUTION. answer in half hr.

Instinctively the problem appears to have more than one solution, but this what I have...
We will divide the ladder into two parts the upper part is (4-x) and the lower part is x.
The distance from the top of the box to the top of the ladder is y.

We have similar triangles created so...

Substituting this for y in the equation above we get..

Which gives four possible solutions for x, but the only two that work are...

So there are two possible distances up the wall the ladder can reach...

Which is the same as Bobbym's answer.

Last edited by Fruityloop (2009-10-14 22:30:35)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: DESPERATELY URGENT HELP NEEDED FOR THIS SOLUTION. answer in half hr.

Hi;

You do nice work, loop!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Fruityloop

Member

Registered: 2009-05-18

Posts: 143

Re: DESPERATELY URGENT HELP NEEDED FOR THIS SOLUTION. answer in half hr.

Thanks for the compliment Bobbym.
One thing I find troubling about this problem is that the problem suggests that it's
impossible to rest a ladder against the upper-outer edge of a box and drag the ladder away from
the box along the ground while keeping contact with the box and wall.
It's mathematically impossible!
I guess it's true but it somehow doesn't 'seem' right.

Last edited by Fruityloop (2009-10-14 22:47:02)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: DESPERATELY URGENT HELP NEEDED FOR THIS SOLUTION. answer in half hr.

Hi Fruityloop;

I was amazed thet there was any solution. The stipulation of touching the box made me think no way, but...

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.