How do you find the angle in the law of cosines?

May 27, 2018

$\cos \left(\gamma\right) = \frac{{a}^{2} + {b}^{2} - {c}^{2}}{2 a b}$

Explanation:

We have
${c}^{2} = {a}^{2} + {b}^{2} - 2 a b \cos \left(\gamma\right)$
so
$2 a b \cos \left(\gamma\right) = {a}^{2} + {b}^{2} - {c}^{2}$
Isolating $\cos \left(\gamma\right)$
$\cos \left(\gamma\right) = \frac{{a}^{2} + {b}^{2} - {c}^{2}}{2 a b}$