[High School - Math] AP summer work help.

[Jtehanonymous]

Hello people of FFR. Over this summer I've been methodically working through my AP summer work for Calculus next year, and I've managed to get down to the problem.

As of right now, however, I've become completly stuck on this last problem. I was hoping to use this thread to post the remaining problems I have, and see if anyone can offer help. (Not answers...I need to know how to actually work everything out..)

So without further ado, here it is:

1. In triangle ABC, where a, b, and c are the measures of the sides,

a + b + c --- ab
________ = _______
2 + √(3) -- a + b - c

Find the measure of angle C.

Okay. How is ANY of this supposed to help me? Is this like, some complicated form of the law of sines or something? I'm so lost, and I'd appreciate something to get started with...=/

And yeah, I don't just want answers...but an explanation. Anyone out there able to help? XD


Thanks,
Jtehanonymous

Edit: Wow, I guess no one can help. XD. Well, my AIM is "Jtehanonymous" if anyone wants to reach me faster...but I'll keep checking back.

Double edit: Okay, I got some help with the word problem I had up, so now it's just that last one I need help with.

Last edit: Yeah, I'm all good now. Thanks Dooty 7.

[dooty_7]

I think I got number 1

first cross multiply to get
(a + b -c)(a + b + c) = (2 + √3)ab
then
a^2 + 2ab + b^2 - c^2 = (2 + √3)ab

This is starting to look close to the Cosine law

c^2 = a^2 + b^2 + (2 - 2 - √3)ab
c^2 = a^2 + b^2 -√3ab

now the Cosine law is
c^2 = a^2 + b^2 - 2abCosC

therefore Cos c = √3 / 2 which is pi / 6 i believe (30 degrees)

I will work on the second part now

[Jtehanonymous]

You do not need to work on the second part, as I already got that before someone posted.

But thank you SO much for your work on the first one, that makes 10X more sense than the way I did it. I still used the law of cosines as well, but I plugged in a = 3 and b = 4 to find c first.

I figured you could just pick out any constants you want, because the equation would always hold true.


But yeah, thanks so much again. XD!

Edit: By the way, your avatar is awesome, bwahahaha.

[dooty_7]

thanks for the avatar compliment and I am always happy to help :P