Question

Find the missing side c in right triangle ΔABC, where a = 5 cm, b = 12 cm, and c is the hypotenuse of the right triangle.

Answer 1

In this problem we want to find the missing side of a right triangle.

We will be able to use something called the Pythagorean Theorem, which states the sum of the squares of a right triangle is equal the square of the hypotenuse.

Long story short, we have this:

In our problem, we are given

$\begin{gathered} a=5 \\ \\ b=12 \end{gathered}$

So we can use them directly in the formula:

$\begin{gathered} a^2+b^2=c^2 \\ \\ 5^2+12^2=c^2 \end{gathered}$

Simplify the left-hand side:

$\begin{gathered} 25+144=c^2 \\ \\ 169=c^2 \end{gathered}$

Finally, we'll need to square root both sides to find the value of c:

$\begin{gathered} \sqrt{169}=\sqrt{c^2} \\ \\ \boxed{13=c} \end{gathered}$

The missing side is 13 cm.