find the length of the unlabeled side. two sides are 12 and 14 .

Let the unknown side be x.
In the given right angled triangle by using Pythagoras theorem ,
[tex]\text{Hypotenuse}^2\text{ = sum of the squares of remaining sides}[/tex]Therefore,
[tex]\begin{gathered} x^2=12^2+14^2 \\ x^2\text{ = 144 + 196} \\ x^2\text{ = }340 \\ x\text{ = }18.44 \end{gathered}[/tex]Thus the unlabeled side is 18.44 units .