In a right triangle, one leg has length $4$ and the other has length $3$. What is the length of the hypotenuse?

Solution Since the triangle is a right triangle, we use the Pythagorean Theorem, with $a=4$ and $b=3$ to find the length $c$ of the hypotenuse. $$\begin{eqnarray} c^{2} &=&a^{2}+b^{2} \nonumber \\ c^{2} &=&4^{2}+3^{2}=16+9=25 \nonumber \\ c &=&\displaystyle\sqrt{25}=5 \nonumber \end{eqnarray}$$ The converse of the Pythagorean Theorem is also true.