Q. 3 - Precalculus Enhanced with Graphing Utilities

Question

If 3 and 4 are the legs of a right triangle, the hypotenuse is _________.

Step-by-Step Solution

Answer

The hypotenuse of the right triangle is 5. 

Step 1. Given information.

In a right angle triangle, the measures of the legs are 3 and 5.

We need to find the hypotenuse of the right triangle.

Step 2. Determine the hypotenuse.

According to the Pythagoras Theorem,

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

Where, $a,b$ are legs and $c$ is the hypotenuse.

Use the above formula to find the hypotenuse.

$\begin{array}{rcl}{c}^2& =& {\left(3\right)}^2+{\left(4\right)}^2\\ c& =& \sqrt{9+16} \left[\because c\nless 0\right]\\ c& =& \sqrt{25}\\ c& =& 5\end{array}$

Step 3. Conclusion.

The hypotenuse of the right triangle is 5.