probrox Posted January 5, 2012 Share Posted January 5, 2012 You only need two triangle, one right agled to work out the length of the isosceles triangle which is the height of the ladder then apply Pythagoras theorem to find out the length of the base Still not getting it. Quote Link to comment Share on other sites More sharing options...
Tyson Posted January 5, 2012 Share Posted January 5, 2012 Still not getting it. see above picture its easier than trying to explain it Quote Link to comment Share on other sites More sharing options...
tbourner Posted January 5, 2012 Share Posted January 5, 2012 But the vertical of the red triangle isn't 3. It would be just over 3 as the ladder would touch the barrel at a few degrees around it, not directly on top. We have no way of knowing how much more than 3 it is. Quote Link to comment Share on other sites More sharing options...
Tyson Posted January 5, 2012 Share Posted January 5, 2012 But the vertical of the red triangle isn't 3. It would be just over 3 as the ladder would touch the barrel at a few degrees around it, not directly on top. We have no way of knowing how much more than 3 it is. My picture isn't accurate as I am naff at drawing but in the original it touches the top exactly. If it didn't it would be impossible to work out. Use a ruler it does touch the top even if at first glance it doesn't look like it does. Quote Link to comment Share on other sites More sharing options...
probrox Posted January 5, 2012 Share Posted January 5, 2012 How did you come to the conclusion that your green triangle was Isosceles, would that not be dependant on the angle of the ladder? Quote Link to comment Share on other sites More sharing options...
Tyson Posted January 5, 2012 Share Posted January 5, 2012 How did you come to the conclusion that your green triangle was Isosceles, would that not be dependant on the angle of the ladder? You could use trig but you can see by looking at it that its an Isosceles triangle plus if it wasn't it again would be impossible to solve. Its just using some maths and a bit of common sense. Quote Link to comment Share on other sites More sharing options...
tbourner Posted January 5, 2012 Share Posted January 5, 2012 That's just silly you're using your eyes to guess the picture rather than maths!! So, which of these horizontal lines is longer: Quote Link to comment Share on other sites More sharing options...
probrox Posted January 5, 2012 Share Posted January 5, 2012 You could use trig but you can see by looking at it that its an Isosceles triangle plus if it wasn't it again would be impossible to solve. Its just using some maths and a bit of common sense. So you assumed? Sorry, i'm not arguing for the sake of it, I just need to prove it to myself now. Quote Link to comment Share on other sites More sharing options...
Tyson Posted January 5, 2012 Share Posted January 5, 2012 I have the right answer and it doesn't ask for working, I could waste an hour to write it all out but I can't be bothered Quote Link to comment Share on other sites More sharing options...
Tyson Posted January 5, 2012 Share Posted January 5, 2012 So you assumed? Sorry, i'm not arguing for the sake of it, I just need to prove it to myself now. Yes but you could prove it if you wanted to but I am not that bothered TBH, I don't mind mate if you want to work it out just have a read of some basic maths books or google to your hearts content Quote Link to comment Share on other sites More sharing options...
Digsy Posted January 5, 2012 Share Posted January 5, 2012 8.796448147 Close, but no. Quote Link to comment Share on other sites More sharing options...
probrox Posted January 5, 2012 Share Posted January 5, 2012 Thats fine, but i'm just struggling to find a trig rule applicable in proving the green triangle is isosceles based on one angle and one side. Quote Link to comment Share on other sites More sharing options...
Tyson Posted January 5, 2012 Share Posted January 5, 2012 Ignore me I am wrong but it was over 6 years since I have done this I was just going by memory but alas it has failed me. I am going to go make some spaghetti to make myself feel better Quote Link to comment Share on other sites More sharing options...
probrox Posted January 5, 2012 Share Posted January 5, 2012 Ignore me I am wrong but it was over 6 years since I have done this I was just going by memory but alas it has failed me. I am going to go make some spaghetti to make myself feel better So much for simple maths and common sense then Still no closer to knowing the answer for sure then. Quote Link to comment Share on other sites More sharing options...
Tyson Posted January 5, 2012 Share Posted January 5, 2012 So much for simple maths and common sense then Still no closer to knowing the answer for sure then. If you ask digsy nicely I am sure he will reveal all. Quote Link to comment Share on other sites More sharing options...
Digsy Posted January 5, 2012 Share Posted January 5, 2012 Ok, here's the solution complete with working out. It didn't occur to me that there might be something special about circles inscribed in triangles until I drew it out on CAD, so I did a quick Google and found the relevant equations. I did pure and applied maths through to A level and was never taught that part. The rest is my own. As you can see, the solution gives two possible answers so you have to use a bit of common sense to decide which is correct - in this case it is obvious. The other answer is how far the other end of the ladder is up the wall. Quote Link to comment Share on other sites More sharing options...
tbourner Posted January 5, 2012 Share Posted January 5, 2012 So it was the sqrt of XYZ over X+Y+Z that we were missing. Interesting. Quote Link to comment Share on other sites More sharing options...
probrox Posted January 5, 2012 Share Posted January 5, 2012 Made sense, thanks. I'll be able to sleep tonight now I've used the formulae shown before but I'm not sure when, and I certainly wouldn't have remembered them to apply to this. Quote Link to comment Share on other sites More sharing options...
Tyson Posted January 5, 2012 Share Posted January 5, 2012 Made sense, thanks. I'll be able to sleep tonight now I've used the formulae shown before but I'm not sure when, and I certainly wouldn't have remembered them to apply to this. i'm like that with cars but not maths, I did it A level and one of my modules at uni was pure maths. I vowed to lay my math skills to rest and join this forum instead Quote Link to comment Share on other sites More sharing options...
tbourner Posted January 5, 2012 Share Posted January 5, 2012 one of my modules at uni was pure maths. I did an Open Uni pure maths module, it was all non-euclidean geometry and stuff though, not triangles and barrels. Quote Link to comment Share on other sites More sharing options...
tbourner Posted January 5, 2012 Share Posted January 5, 2012 Ooh look: http://www.pjwatsonz.com/wp-content/uploads/Over-a-barrel-A-solution.pdf Quote Link to comment Share on other sites More sharing options...
Pixelfill Posted January 5, 2012 Share Posted January 5, 2012 Ooh look:http://www.pjwatsonz.com/wp-content/uploads/Over-a-barrel-A-solution.pdfTrev I could kiss you, this has been driving me mental all day. The question is did Stephen get it right edit: hadn't seen digsy's post:thanku: - so Stephen did get it right - was it luck or is he a genius Mike Quote Link to comment Share on other sites More sharing options...
Digsy Posted January 5, 2012 Share Posted January 5, 2012 Ooh look: http://www.pjwatsonz.com/wp-content/uploads/Over-a-barrel-A-solution.pdf That's a helluva lot more simple than my method Quote Link to comment Share on other sites More sharing options...
Pixelfill Posted January 5, 2012 Share Posted January 5, 2012 That's a helluva lot more simple than my method It's the same algebraic solution as yours, just some smart arse can solve quadratic equations in their head ! Their arithmetic solution was a bit of a leap of faith really, they just happened to know off the top of their head some right angle triangle dimensions. You're still my hero Mike Quote Link to comment Share on other sites More sharing options...
Tyson Posted January 6, 2012 Share Posted January 6, 2012 I did an Open Uni pure maths module, it was all non-euclidean geometry and stuff though, not triangles and barrels. Mine was all about numbers and proofs, never again !! Quote Link to comment Share on other sites More sharing options...
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