Question

If a right triangle has a hypotenuse of $13$ inches and a leg of $5$ inches, How could you use the Pythagorean Theorem to find the missing side? What is the length of the missing side?

Answer 1

To find the missing side, using Pythagorean Theorem:

In the right triangle, Hypotenuse $=13$ inches, one leg $=5$ inches.

Let $x$ be the other leg.

Apply the Pythagorean Theorem and calculate the missing side in below:

$\begin{array}{rcl}{\left(\text{Hypotenuse}\right)}^2& =& {\left(\text{One leg}\right)}^2+{\left(\text{Other leg}\right)}^2\left(\text{Pythagorean Theorem}\right)\\ & \Rightarrow & {13}^2=5^2+x^2\left(\text{Hypotenuse}=13,\text{One leg}=5\right)\\ & \Rightarrow & 169=25+x^2\left(\text{Simplify}\right)\\ & \Rightarrow & x^2=169-25\\ & \Rightarrow & x^2=144\\ & \Rightarrow & x=\sqrt{144}\left(\text{Take square root}\right)\\ \therefore x& =& 12\end{array}$

Therefore, the other leg is $12$ inches.

Hence, the length of the missing side is $\mathbf{12}$ inches.