This is why you need to listen in highschool math

I'm in the middle of preparing the loot-bags for Dumpling's bday party on Thursday (5! FIVE!!!!!) and I want to attache a little paper ball to each. I found the pattern on Heather Bailey's fabulous website. And because I wanted this to go fast, since I have to make 20, I bought a circle hole punch.

She has a fabulous pattern all worked out for a 5inch or 6.5inch FINISHED ball, but I need to scale it to work with my 5 cm punch. I have no idea why size ball I`m going to end up with, but it`s going to be smaller, because my circle is smaller than hers, which is fine.

Here is the thing. I am a math moron. I know my circle is 5 cm in diameter. Which I can work out to have a radius of 2.5 cm, or a circumference of 15.7 cm because the only thing I remember from geometry is C= Pi*D

But now I need to calculate the sides of my triangle. I know it's an equilateral triangle. And I pretty much figured out that inside the big equilateral triangle there are 3 Isosceles triangles with 2 sides of 2.5 cm and an angle of 120...... but I'm stumped! How do I calculate the sides of the triangle, so that I get a perfect equilateral triangle inside my circle?

If I haven't lost you yet and you know how to help me, PLEASE!!!! I tried Google but either the formulas don't work or I'm too dumb to figure it out....

AND THE ANSWER IS:

4.4 cm, which you can figure out by either:

Law of cosines= c*squared = a*squared plus b*squared - 2abCOS(C) so, Equilateral Triangle Side = 2.5*squared + 2.5*squared - 2(2.5)(2.5)Cosine(120degrees)

OR: scale the damned .jpg to 5cm and print it!!!!! thanks OmegaMom for coming up with a solution that was staring me in the face!

Clearly, Mila didn't read the last sentence when I wrote that I was too dumb to follow the formula!!! (also, how cool is that? mila is a former staffer who is sorely  missed now that she is busy doing some fancypants graduate degree in an other town, but still keeps up by reading my blog!)

Comments

[Johnny]

This gives the partial answer:

http://answers.yahoo.com/question/index?qid=20071025170634AAbLsgi

Sorry I can't do the math right now, I have to run. If you haven't got it worked out by tonight, I'll do the math. So, the comment is also a placeholder (for me).

[Shannon]

Why can't you reduce (via copier) the size of the pattern to the size of your current circle? This way, no math.

Perhaps I'm making this too easy?

[Mrs Figby]

All *I* remember from geometry is the Pythagorean Theorem, which is for non-equilateral triangles. So can't help you. I tried Brainiac, but he doesn't know either. I'll bet Zen knows, because Zen is Gifted (say that in a snotty, braggy, suburban mom voice) in math. If you don't have an answer by the time he gets home, I'll ask him.

Hey, I bet omegamom or spacemom could help. They're math-y types. Or Harry D'Eyeball. Except he's frantically busy right now trying to bring our mail server (in Seattle) back up, so I'm guessing you won't hear from him anytime soon. Especially if you email him. (Har!)

[OmegaMom]

Check your email.

[Mila]

Ok: Law of cosines= c*squared = a*squared plus b*squared - 2abCOS(C)

so, Equilateral Triangle Side = 2.5*squared + 2.5*squared - 2(2.5)(2.5)Cosine(120degrees)

With no calculator, that's the best I can do... hope it helps!

-Mila

[Alyssa]

Totally delurking to throw something out there. Isn't is all about ratios? If the pattern has is for a 5 inch circle and the side of the triangle is x inches, wouldn't it work that for a 5 cm circle, that the side of the triangle is the same number but just substitute centimeters for inches? This is going to bug me all day. It's been a long time since high school geometry.

[kris]

well, now i know i am stupid...

[Mila]

NOW who's having a popular day? ;)

[beverly]

Yeah I would be totally clueless too. Cute balls though if you really were able to get them done. Looks almost like the Guangxi Love Balls!

Beverly