A triangle is a right triangle if it satisfies the pythagorean theorem:
[tex]\begin{gathered} c^2=a^2+b^2 \\ where\colon \\ c>a,c>b \\ so\colon \\ for\colon \\ a=5 \\ b=12 \\ c=13 \\ 13^2=5^2+12^2 \\ 169=25+144 \\ 169=169 \\ This_{\text{ }}is_{\text{ }}_{}true \end{gathered}[/tex]Therefore, the answer is C
