Can anybody display the maths?

1. Jan 5, 2012

rob4586

From another forum

Can you work this one out?

http://i44.tinypic.com/2hxu71s.jpg

It's supposed to be a ladder resting on a barrel. We've guessed the answer will be 12ft, and proven it with CAD! What the maths behind it?

2. Jan 5, 2012

rob4586

I'd of thought that there isn't enough information there to give an answer! A height would have to be known? :s

3. Jan 5, 2012

Number Nine

A height is known. Look carefully.

4. Jan 5, 2012

Staff: Mentor

there's enough info although it can't be solved simply thru geometry and algebra. You basically have three constraints:
1) ladder top constrainted to move along y-axis (ie xtop=0 and 0<ytop<12.5)
2) ladder bottom constrainted to x-axis (ie 0<xbot<12.5 and ybot=0
3) ladder is tangent to circle

you can use the pythagorean theorem to relate xbot and ytop to the 12.5

you need an equation for constraint #3

5. Jan 5, 2012

rob4586

You've obviously got its height of 3 at a depth 1.5 from the y axis. So would you have to use the equation of the circle and then differentiate it?

6. Jan 5, 2012

rob4586

I've considered similar triangles but as previously mentioned there isn't the correct info there I don't think.

7. Jan 5, 2012

rob4586

Sorted it, can be done with Pythagoras!

8. Jan 5, 2012

Staff: Mentor

solved it right?

"Sorted it" sounds like something from Harry Potter's sorting hat.

Also could you tell us how you did it.

9. Jan 6, 2012

rob4586

Attached the file of the workings, it almost was magic :p

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10. Jan 6, 2012

D H

Staff Emeritus
Very nice, using the equation for the radius of an inscribed circle. Much simpler than solving for the angle.