A Maths Problem Hmm.

Ok I have a question in a maths assignment that I am a little confused about.

The question asks me to a draw a diagram of a 3 metre ladder against a brick wall that has a 1.8 metre gap between the bottom of the wall and the bottom of the ladder.

Ok fairly simple to do.

It then asks me to find the the space between the bottom of the wall and the top of the ladder.

So me and my misses take a look at the diagram and go, "oh a right triangle, pythagoras theroum eh".

So my misses has a look around and try's to remember how it works and even try's a few online calculators to try and work it out.

But always the answer came to 3.4 metres...... well.. uh... Let's say I'm 6 foot tall and lean on a moderate angle into a wall, there is certainly not a 6 ft gap between the wall bottom and my head let alone a larger gap then my height.

So I went ahead and conducted my own test just using a rollie paper packet (I also tested with a ruler) as a ladder and using one of those basic tape measures they use for material.

This way I would have the gap between the wall bottom and the top of the packet and simply need to find a formula to work out the answer, this way I could do the same for my math problem.

I measured the height of yhe rolly paper packet which was an approx 7cm, I then placed it on an angle like a ladder against the wall and measures the gap which was an approx 4.5cm. I then proceeded to measure the gap between the wall bottom and the top of the rolly paper packet which was an approx 5cm's.

So basing the object height as H, the flat floor gap as G and the vertical gap between the wall and top of object as R, here is what I did:

H^2 = 49.
G^2 = 20.25.

49 - 20.25 = 28.75.

R = Square Root of 28.75 which equals an approx 5.3cm.

Which leads me to believe this way of working it out is more or less correct. I tested a second time with a larger object to see if I got around about the same result (it wasn't perfectly accurate on either occasions due to using the tape measure and the wall etc).

I did this on my math question and ended up with the answer of 2.4 metres which sounds much more reasonable and realistic to me.

But my misses and even a few others I know are convinced that I am most likely wrong. But logically how can a leaning object be higher then it's tallest point...... the ladder for example, it's impossible to a degree *shrugs*.

Wow long post.... anyway hope someone actually reads through and understands this heh.

 

 

 

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Chesso, you are right that this math problem applies the Pythagorean theorem. You are also right that the length of the ladder must be the longest of all three sides. The problem I found in your statement above was in the use of the formula. You were very close.

The formula is a2 + b2 = c2 (or h2 + g2 = r2) and NOT h2 - g2 = r2. The longest side of the right triangle is c. As for your answer with the ladder, the height from the ground to the top edge is indeed 2.4 meters.

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Ok I tried the formula of a2 + b2 = c2, or rather I plused a2 and b2 together and got the square root of the answer which gave me again 3.4 metres.

The only way I can get a formula to get the correct answer is my way so I'm still confused lol.

Iv'e done quite a bit of pythagoras but I forget these things so quick and I remember there being a fair few slight variations to certain situations where it was handles slightly different from other methods.

Here is how I just did it based on a basic tutorial and using google calculator heh heh:

x^2 = 3^2 + 1.8^2
= 9 + 3.24
= 12.24
x = Square root of 12.24
x = 3.49857114

So basically 3.4, or rather 3.5 with rounding.

Which by the nature of the question is impossible lol.

Unless they wrote the question wrong and wanted the area *shrugs*.

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When applying the Pythagorean theorem on a right triangle, you must first define your variables. In the case of your ladder question, ( a ) is the distance between the foot of the ladder and the wall, ( b ) is the height between the ground and the top of the ladder, and ( c ) is the length of the ladder. Remember that ( c ) is the longest side of the triangle (or the one that is at an incline).

So . . . in your question, a = 1.8 and b = unknown and c = 3.

a^2 + b^2 = c^2
1.8^2 + b^2 = 3^2
3.24 + b^2 = 9
b^2 = 9 - 3.24 = 5.76
b is the square root of 5.76 or 2.4.

Does that sound more reasonable? You had the question down from a conceptual standpoint. It was only an issue of assigning variables. I hope this helps. If you have any more questions, feel free to ask or PM me.

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Has anyone pointed out yet that "maths" is not a word?
It's math BTW

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A Google search of maths seems to say you are wrong

Ahh yes longest side haha woopsy.

Oh well atleast I got the right answer but I better fix that up. I'm used to the longest side not being present and completely missed it.

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Oh, it's the british way. I get it.
But i'd like to point out that more people say "math" than "maths", and also the ths phoneme sounds wierd

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Awww, I'm used to saying and hearing it.

But I use both quite randomly for some reason *shrugs*.

Oh well atleast I'm getting better with more important grammar and such, you should have seen how bad I was just a few years ago.

Oh and I got the *math* all fixed up now. Just two more annoyingly large questions to go and I can send it off and not have to worry about anymore maths.

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Anyway I was mostly just messing with you
Even though I'm in Honors I never really found that I was that good at math, but good luck in all your endeavors and I will help if you have another question which I know the answer to! I could have done this one but everyone else had it covered and I felt like posting
(Sux that you're doing it while we are just finishing our summer break here in the US.)

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Haha, well after these last 2 math questions and doing my science portfolio and oral report I'm done for the year .

The last 2 questions I have are a little big, something along the lines of:

"Mr X has a paddock that is big and 80 metres along one side and this other side has a pond and some other things"....

"Draw a diagam of the paddock and relevant information"

"Find the diameter blah blah"

"If this, than what is this blah blah".

For the most part it's drawing the diagram I have a problem with, I'm used to working with a digram pre-drawn not drawing it myself and then working it out lol.

And than theres another one that is similar. The rest I managed mostly on my own but man did I have to go back through previous work to remember how to half of it

 

 

 

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