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Q. 1

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Found in: Page 380

### Precalculus Enhanced with Graphing Utilities

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

# Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.In a right triangle, with legs$a$ and $b$and hypotenuse$c$, the Pythagorean Theorem states that _________.

In a right triangle, with legs$a$and $b$and hypotenuse$c$, the Pythagorean Theorem states that${c}^{2}={a}^{2}+{b}^{2}$.

See the step by step solution

## Given information

In a right triangle, with legs $a$and localid="1646398075821" $b$ and hypotenuse $c$, the Pythagorean Theorem states that _______________.

The main objective is to fill the blank with correct value.

## Theorem:

According to the Pythagorean theorem, for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs of the triangles.

Here, the lengths of the two legs are $a$ and $b$ and the length of the hypotenuse is $c$.

Then by the Pythagorean theorem,

$\begin{array}{rcl}{\mathrm{Hypotenuse}}^{2}& =& \mathrm{leg}{1}^{2}+\mathrm{leg}{2}^{2}\\ {c}^{2}& =& {a}^{2}+{b}^{2}\end{array}$

So, the blank will be filled with ${c}^{2}={a}^{2}+{b}^{2}$.