trouble with Cosine Rule

[procyon]

Hi,

I had this equation

x² = a² + b² - c²

these figures fit the equation

a=10, b=5, c=2 giving x=11

121 = 100 + 25 - 4

then it occured to me that the original equation looked very like the Cosine Rule

c² = a² + b² - 2ab Cos(c)

so that

2ab Cos(c) = a² + b² - c²

so combining this with my original equation I would have thought

x² = 2ab Cos(c)

which it doesn't ¿ 2 x 10 x 5 x Cos(2) = 99.94......

What did I miss or misunderstand ¿

Many thanks,

Pro

 

[pka]

I had this equation
x² = a² + b² - c²
these figures fit the equation
a=10, b=5, c=2 giving x=11
121 = 100 + 25 - 4
then it occured to me that the original equation looked very like the Cosine Rule
c² = a² + b² - 2ab Cos(c) so that
2ab Cos(c) = a² + b² - c²
so combining this with my original equation I would have thought
x² = 2ab Cos(c)
which it doesn't ¿ 2 x 10 x 5 x Cos(2) = 99.94......
What did I miss or misunderstand ¿

You have confused the \(\displaystyle c~\&~C\).
The law of cosines is \(\displaystyle c^2=a^2+b^2-2ab\cos(\theta),\) where \(\displaystyle \theta\) is the angle between the sides with lengths \(\displaystyle a~\&~b\).
You used \(\displaystyle c\) for \(\displaystyle \theta\) they are different.

 

[procyon]

Thanks pka, that clears it up for me

btw, had just realised also that you can't have a triangle with sides 10, 5, 2, lol

thanks again

pro