You have a right triangle and the length of the legs, use Pythaorean theorem to find the length of the hypotenuse (AB)
[tex]\begin{gathered} AB^2=AC^2+BC^2 \\ \\ AB=\sqrt[]{AC^2+BC^2} \\ AB=\sqrt[]{10^2+15^2} \\ AB=\sqrt[]{100+225} \\ AB=\sqrt[]{325} \\ AB=18 \end{gathered}[/tex]Then, the length of AB is 18