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Q. 1

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Precalculus Enhanced with Graphing Utilities

Found in: Page 380

Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

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 $c^{2} = a^{2} + b^{2}$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

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,

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

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

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