Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Appendix F - Exercise Set: 33

Answer

$12$

Work Step by Step

According to the Pythagoras Theorem, if $a$ and $b$ are the lengths of the legs of a right triangle, and $c$ is the length of the hypotenuse, then $a^{2}+b^{2}=c^{2}$. Since $a=5$ and $c=13$, we substitute these values in the formula and solve: $c^{2}=a^{2}+b^{2}$ $13^{2}=5^{2}+b^{2}$ $169=25+b^{2}$ $b^{2}=169-25=144$ Therefore, $b=\sqrt (144)=12$ Since $b$ represents a length, we assume that $b$ is positive and is equal to $12$.
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