# Math Help - law of cosines

1. ## law of cosines

consider a triangle with known sides a=0.5, b=2, and c=0.5, how could i use law of cosine to find an unknown angle between sides a and b, i tried to use law of cosine it gave me cos(ab)=2, which is impossible

2. Originally Posted by aukj
consider a triangle with known sides a=0.5, b=2, and c=0.5, how could i use law of cosine to find an unknown angle between sides a and b, i tried to use law of cosine it gave me cos(ab)=2, which is impossible

This is an impossible triangle. It does not conform to the triangle inequality!

3. Originally Posted by aukj
consider a triangle with known sides a=0.5, b=2, and c=0.5, how could i use law of cosine to find an unknown angle between sides a and b, i tried to use law of cosine it gave me cos(ab)=2, which is impossible

The Cosine Rule states that

$c^2 = a^2 + b^2 - 2ab\cos{C}$.

In your case, $a = \frac{1}{2}, b = 2, c = \frac{1}{2}$.

So by the Cosine Rule...

$\left(\frac{1}{2}\right)^2 = \left(\frac{1}{2}\right)^2 + 2^2 - 2\left(\frac{1}{2}\right)(2)\cos{C}$

$\frac{1}{4} = \frac{1}{4} + 4 - 2\cos{C}$

$0 = 4 - 2\cos{C}$

$2\cos{C} = 4$

$\cos{C} = 2$.

You are correct, this equation can not be solved. That means that this triangle does not exist... This is easily verified by the triangle inequality...

4. thanks