i am studying for math at the moment and I am stuck a bit with the derivation of the law of cosines. First of all, sorry if i mention some things wrong, I study in german so it could be that we name some things different. :-)

My problem is that i don't know how to go on after a certain step. It would be cool if you could point me in the right direction .

Problem:

Derive the law of cosines from a triangle made of 2 vectors

**a**= { ax, ay az }

**b =**{ bx, by, bz }

**c**=

**b - a**

All lengths are unknown and arbitrary.

So, we are looking for

**c**,

**alpha, beta & gamma**

**alpha**is between c and b

**beta**is between c and a

**gamma**is between a and b

the longest side is c which can be separated into

**p**and

**q**which will give me two right angled triangles.

From this information i can easily get

cos alpha = p / b ->

**p = b * cos alpha**

cos beta = q / a ->

**q = a * cos beta**

**c = p + q**

**c = b * cos alpha + a * cos beta**

so far so good ^-^

In the book is written that I

**shall do the same for the sides a and b**. And that is were i get stuck. All the time i am calculating the same stuff on and on again but i am not able to go one step further. It seems that i am missing some variable or s.th.

Lets say the

**opposite leg of alpha is h**

so b = sqrt ( p * p + h * h )

p = cos alpha * b

h = ??? <- how

i ??

The goal is to get

c*c = a*a + b*b - 2ab*cos

**gamma**