Question

Find the length of the third side. If necessary, write in simplest radical form.DV895

Answer 1

In order to solve the missing side for a right triangle, we can use the Pythagorean theorem

$a^2+b^2=c^2$

then, we rewrite the expression for on of the sides different from the hypotenuse

$\begin{gathered} a^2=c^2-b^2 \\ a=\sqrt[]{c^2-b^2} \end{gathered}$

replace with the values

$\begin{gathered} a=\sqrt[]{(\sqrt[]{89})^2-5^2} \\ a=\sqrt[]{89-25} \\ a=\sqrt[]{64} \\ a=8 \end{gathered}$