Answer
Refer to the step by step section below.
Work Step by Step
Assume I have $A,a,b$ given (works similarly for other cases.)
By the Law of Sines($\frac{{\sin {A}}}{a} = \frac{{\sin {B}}}{b} = \frac{{\sin {C}}}{c}$) I can get one of the other two angles. (Here $\sin {B}=b\frac{{\sin {A}}}{a}\\B=\sin^{-1}{(b\frac{{\sin {A}}}{a})}.$
Then as we know the sum of the $3$ angles is $180^o$ so I count the third degree by subtracting the sum of the know two angles from $180^o$. (Here $C=180^o-(A+B).$
Finally, by the Law of Sines I can get the final side. (Here: $c=b\frac{{\sin {C}}}{\sin {B}}).$