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Q. 3

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Found in: Page 13

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

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

The hypotenuse of the right triangle is 5.

See the step by step solution

## 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.

role="math" localid="1645771268022" $\begin{array}{rcl}{c}^{2}& =& {\left(3\right)}^{2}+{\left(4\right)}^{2}\\ c& =& \sqrt{9+16}\left[\because c\nless 0\right]\\ c& =& \sqrt{25}\\ c& =& 5\end{array}$

## Step 3. Conclusion.

The hypotenuse of the right triangle is 5.