Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 10 - Geometry - 10.2 Triangles - Exercise Set 10.2 - Page 627: 26


$a=12$ ft

Work Step by Step

RECALL: The Pythagorean Theorem states that in a right triangle, $c^2=a^2+b^2$ where $c$ = length of the hypotenuse $a$ and $b$ are the lengths of the two legs. The given triangle has: $b=5$ ft $c=13$ ft Use the Pythagorean Theorem above to obtain: $c^2=a^2+b^2 \\13^2=a^2+5^2 \\169 = a^2 + 25 \\169 - 25=a^2 \\144=a^2$ Take the square root of both sides to obtain: $\pm \sqrt{144} = a \\\pm \sqrt{12^2} = a \\\pm 12=a$ Note, however, that $a$ represents a length, so it cannot be negative. Thus, $a=12$ ft.
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