Finding the Hypotenuse of a Right Triangle

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.