Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**Anakin****Member**- Registered: 2009-10-04
- Posts: 145

Quick question in case anyone is awake at this time.

A tool shed, 250 cm high and 100 cm deep, is built against a wall. Calculate the shortest ladder that can reach from the ground, over the shed, and to the wall behind.

Here's my attempt:

Letting y=the length of ladder: The length before the ladder touches the shed's top = 2.5/cos(v) and the other length = 1/cos(u).

y=2.5/cos(v) + 1/cos(u)

y'=2.5sin(v)/[cos(v)]^2 + sin(u)/[cos(u)]^2

I'm not sure where to go from there. I did this stuff so long ago, it's out of memory. Any hints?

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,602

Hi Anakin;

I formed the equation: Where y is the length of the ladder.

Set that equal to 0 and solve for theta

Plug it back into the original equation.

x = 479.1149 cm

This is straight from my notes, but I remember this problem. I google for it and come up with this.

http://ca.answers.yahoo.com/question/in … 608AAWEw2N

I have a numerical solution that is more interesting.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

**Online**

**Anakin****Member**- Registered: 2009-10-04
- Posts: 145

And that is the correct answer!

Let me try to comprehend what you did there. http://i46.tinypic.com/2l9gsvl.png

Was that correct analysis?

I forgot that the angle at the bottom is the same as the second angle I pointed (or you did) out in the middle of the diagram.

Oh boy, thanks a lot once more Bobby.

Edit: Didn't see the link you posted. Interesting. And I guess he likely had the same question from the textbook as well.

*Last edited by Anakin (2010-06-24 21:34:26)*

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,602

Hi Anakin;

Yes, had the answer written down already. He does it slightly different in the link I found. Using Calculus on it is overkill.

What is your textbook?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

**Online**

**Anakin****Member**- Registered: 2009-10-04
- Posts: 145

Sorry for the late reply, didn't see the last part of your post. As for the question, I'm not so sure of the name. We just get sheets photocopied from the same book. I'll let you know when I get back today from the dreadful exam. 8-)

Edit:Typo.

*Last edited by Anakin (2010-06-24 22:25:13)*

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,602

Hi Anakin;

Okay, and good luck again.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

**Online**

**Bob123445****Guest**

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,602

Hi;

Your latex is not showing correctly.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

Pages: **1**