Proof for Law of Cosines?

MathIsGreat · P versus NP Offline Joined: 20 Jan 2008 Posts: 32

You know on the left hand side there are links that lead you to various places on the site?
And under those links there is some interesting formula or something?
There is a proof or something about the Law of Cosines.
I try to follow it, but I don't understand.
Can someone help?
Thanks.

**Posted:** Tue Nov 03, 2009 8:58 pm

harwi · P versus NP Offline Joined: 18 Apr 2008 Posts: 34

make it into 2 right angle triangle and then find the height of the triangle. after that subsitute to find the side. Try...
thx

**Posted:** Tue Nov 03, 2009 9:36 pm

MathIsGreat · P versus NP Offline Joined: 20 Jan 2008 Posts: 32

I'm not sure what you mean... Question

**Posted:** Wed Nov 04, 2009 8:45 pm

bbgun34

Explaining the 'proof without words' on the site:

Consider a triangle with sides a,b,c, and angle $\theta$ on point C. Draw a circle about B with radius a. Draw the diameter extended from AB; you get the radius a and the length a-c, since we subtract c from the radius in the opposite direction. Now, extend BC in the original triangle to make the diameter; we get a right triangle when we extend AC. By the definition of cosine, the length from C to where the extension of AC meets the circle again is $2a\cos{\theta}$ . We subtract b from this to get the length of the extension that is not on ABC. Now we use Power of a Point to get
$(2a\cos{\theta}-b)(b)=(a+c)(a-c)$
$2ab\cos{\theta}-b^2=a^2-c^2$
$c^2=a^2+b^2-2ab\cos{\theta}$ .

The animation is a way more concise way of putting this. Hope this made any sense at all... maybe

**Posted:** Wed Nov 04, 2009 9:24 pm

_________________
Bomb

4+6+4x6=34; $2^5=(2^2)!+2^3$
$\prod \sum \square \ge \square \sum \prod$

AndrewTom

Hi. There are some proofs of the cosine rule here: http://en.wikipedia.org/wiki/Law_of_cosines

Hope this helps you.

**Posted:** Thu Nov 05, 2009 12:21 am

Poincare

http://lmgtfy.com/?q=law+of+cosines+proof

**Posted:** Thu Nov 05, 2009 6:46 pm

_________________
Please visit this website: freerice.com and play for just 5 minutes and help end hunger.