Can anybody display the maths?

[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?

 

[rob4586]

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

 

[Number Nine]

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

A height is known. Look carefully.

 

[jedishrfu]

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

 

[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?

 

[rob4586]

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

 

[rob4586]

Sorted it, can be done with Pythagoras!

 

[jedishrfu]

Sorted it, can be done with Pythagoras!

solved it right?

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

Also could you tell us how you did it.

 

[rob4586]

solved it right?

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

Also could you tell us how you did it.

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

 

[D H]

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