Verified answer

You solve for cosθ first and then take inverse of cosθ .

θ = arc cos [(a^2+b^2-c^2)/(2ab)]

of course you can solve it if the sides a and b are given and an angle C is also defined...if that's the case, you just direct substitute the respective variables to the formula.

c^2=a^2 + b^2 -2ab cosθ

subtract a^2 and b^2 for both sides

c^2 - a^2 - b^2 = -2ab cosθ

divide -2ab for both sides

(c^2 - a^2 - b^2) / -2ab = cosθ

take a cos^-1 for both sides

θ = cos^-1 { (c^2 - a^2 - b^2) / -2ab }

make cosθ the subject of formula. then substitute the value of a.b. and c into the equation.