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.
Applying this theorem to triangle ABC (see the above diagram):
[tex]AC^2=AB^2+BC^2[/tex]
Substituting with AB = 10 cm, BC = 15 cm, and solving for AC:
[tex]\begin{gathered} AC^2=10^2+15^2 \\ AC^2=100+225 \\ AC^2=325 \\ AC=\sqrt[]{325} \\ AC\approx18\operatorname{cm} \end{gathered}[/tex]
