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
please help
The Cosine Rule states that
$\displaystyle c^2 = a^2 + b^2 - 2ab\cos{C}$.
In your case, $\displaystyle a = \frac{1}{2}, b = 2, c = \frac{1}{2}$.
So by the Cosine Rule...
$\displaystyle \left(\frac{1}{2}\right)^2 = \left(\frac{1}{2}\right)^2 + 2^2 - 2\left(\frac{1}{2}\right)(2)\cos{C}$
$\displaystyle \frac{1}{4} = \frac{1}{4} + 4 - 2\cos{C}$
$\displaystyle 0 = 4 - 2\cos{C}$
$\displaystyle 2\cos{C} = 4$
$\displaystyle \cos{C} = 2$.
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...