# trouble with Cosine Rule

• Aug 14th 2011, 02:55 PM
procyon
trouble with Cosine Rule
Hi all,

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
• Aug 14th 2011, 03:01 PM
anonimnystefy
Re: trouble with Cosine Rule
hi procyon

it shouldn't be cos(c) but in there should be an angle opposite to the side c in the triangle with sides a,b and c.
• Aug 14th 2011, 03:14 PM
procyon
Re: trouble with Cosine Rule
Quote:

Originally Posted by anonimnystefy
hi procyon

it shouldn't be cos(c) but in there should be an angle opposite to the side c in the triangle with sides a,b and c.

Wow, thanks for the quick reply :)

Not sure that I understand you though :(

I'll put the equations together

a² + b² - c² = x²
a² + b² - c² = 2ab.Cos(c)

Surely 2ab.Cos(c) must equal x² for any given a, b & c (10, 5 & 2 in this case)

hmmm...
just had a thought, a triangle can't have sides 10, 5 & 2. Is this perhaps where it falls down?
• Aug 14th 2011, 03:24 PM
Plato
Re: trouble with Cosine Rule
Quote:

Originally Posted by procyon
Wow, thanks for the quick reply :)
Not sure that I understand you though :(
I'll put the equations together
a² + b² - c² = x²
a² + b² - c² = 2ab.Cos(c)
Surely 2ab.Cos(c) must equal x² for any given a, b & c (10, 5 & 2 in this case)

It is easy: you are missing the point.
In that formula: $c^2=a^2+b^2-2ab\cos(C)$ you have different variables, $c~\&~C$ and $c\ne C$.
• Aug 14th 2011, 03:31 PM
procyon
Re: trouble with Cosine Rule
Quote:

Originally Posted by Plato
It is easy: you are missing the point.
In that formula: $c^2=a^2+b^2-2ab\cos(C)$ you have different variables, $c~\&~C$ and $c\ne C$.

Hi Plato,

Many thanks for clearing that up for me. That's the trouble when you suddenly remember a formula through the mists of time :(

I had thought 2ab.Cos(c) not 2ab.Cos(ø)

thanks again