The Pythagorean theorem states:
[tex]c^2=a^2+b^2[/tex]
where a and b are the legs and c is the hypotenuse of a right triangle.
Substituting with c = 13, and a = 4, and solving for b (the third side):
[tex]\begin{gathered} 13^2=4^2+b^2 \\ 169=16+b^2 \\ 169-16=b^2 \\ 153=b^2 \\ \sqrt[]{153}=b \\ \sqrt[]{9\cdot17}=b \\ \sqrt[]{9}\cdot\sqrt[]{17}=b \\ 3\sqrt[]{17}=b \end{gathered}[/tex]
