posted
I am positive I learned this in the ninth grade and knew it for a significant portion of time after that, but, ya know...

So I've got a triangle. I've got a short leg of the 'L' and the long leg of the 'L'. I need to know how long that diagonal line is that connects them. I know, I know. That was worse than a grade schooler. Feel free to point and laugh.

Thanks for any help!
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It's a right triangle? The sum of the squares of the "legs" equals the square of the "diagonal" - (long L)^2 + (short L)^2 = (diagonal)^2
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posted
The pythagorean theorem will work if it is a right triangle.

If not, you could use the law of cosines. Here is an applet that will calculate the length for you if you know the angle that the long and short side make:

posted
haHA! Thanks kaioshin for the link. Entering things into text boxes and clicking links is easy. Unfortunately, pretty much everything the rest of you said went miles over my head, but thanks anyway!.

Oh man I'm pathetic.

*goes to cry in a closet*
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posted
Couldn't award points. Frictionless surface: the elephant would slide into the spring after being hit by the block. After it swam out of the spring, that'd be one enraged elephant on your hands. Everyone knows that a rampaging elephant is a bigger problem than a block sliding down a ramp. And that you don't solve a small problem by creating a bigger one.

posted
Well... it seems to me that you're suffering more from a bad memory rather than being bad at math. It's old Pyth, sure, but either you remember that or you don't. If you don't, it's not as though you're going to be deriving it. At any rate, I'd probably take a day or so to figure out the derivation, and I'm supposed to be good at this sort of thing. (Geometry was never my strong suit, admittedly.) I might actually find it easier to derive the cosine rule and get Pyth as a special case, come to think of it. Integrals with trig, yes, much easier. I could likely do that in a few hours.
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posted
vonk, dear, I have to get myself a class which I just don't care about, and do something similar. That made my quarter-hour! (You've made these 15 minutes more exciting than they would have been otherwise ^^;;.)

The scary thing, however, is that I think I could solve this one. Potential energy = MGH, and um, something 1/2MV^2, then kx, and yeah, given enough time, a calculater, a geek, and three diet soda cans, I could solve it.

Oh, wait, no. There's an elephant in the way!

Major slops to the teacher for having the comma slip lines. Not cool!
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quote:Originally posted by King of Men: I might actually find it easier to derive the cosine rule and get Pyth as a special case, come to think of it.

Without a doubt.

EDIT: Actually, I take that back. You need the Pythagorean Theorem to derive the Law of Cosines, even though you can later point out that the Pythagorean Theorem is a special case of it.
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posted
No, there's a proof from pure trig relations, though admittedly I was thinking of how to calculate an area when I posted that.
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posted
haha I just got an email that had a whole bunch of those, including the elephant and the "find x" in it. Made me really tempted to do throw my stats test, but I actually do need that class.
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posted
There's an excellent math site at WebMath.com, which may or may not be helpful. (The "right triangles" page is under "the Trig. & Calculus" tab.)
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posted
I'd love to see more myself. I'll bet I've heard most of these; I've seen the "find X" one before and heard various other mathematical jokes of the sort you posted, but I haven't heard that specific one, nor have I see the Elephant one. So if there's a compilation that I haven't seen, I'd like to look at it!
Posts: 142 | Registered: Apr 2005
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posted
Ha! The 'Find X' one is great. That seems more like something I would answer. If any of you misunderstood, the elephant answer isn't mine, I found it on the web. Sorry if I wasn't clear.

In school, if I wanted to be snotty and didn't know an answer, I'd usually just give some sarcastic exhistensial argument. Something like "The box, the ramp and the spring are all constructs of you unique perspective, and are thus unknowable from my perspective, so the answer is 'c: none of the above.'" (regardless of whether it is multiple choice or not) I don't think I ever got any points for those, but mighta gotten a smiley face next to my 'F-'.
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quote:Originally posted by vonk: Also, this seems like an appropriate place to post this. That is probably the exact same way I would answer the question.

quote:Originally posted by King of Men: I might actually find it easier to derive the cosine rule and get Pyth as a special case, come to think of it.

Without a doubt.

EDIT: Actually, I take that back. You need the Pythagorean Theorem to derive the Law of Cosines, even though you can later point out that the Pythagorean Theorem is a special case of it.

How hard it is to prove depends on what you start with. Me? I like to start with linear algebra.

It's really simple there - the law of cosines is a direct application of the DEFINTION of cosine, with the added bonus of the Pythagorean theorem as a special case.

What I really like about the linear algebra perspective is it VERY easily generalize to any finite dimensional case.

In other words, the law of cosines (and the Pythagorean theorem) aren't some fluke of living in a 3 dimensional world, or some weird effect that only occurs in 2d - they hold in ALL (finite) dimensions.

EDIT: The elephant thing made my night. Thanks!
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