Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 8 - Right Triangles and Trigonometry - 8-1 The Pythagorean Theorem and It's Converse - Practice and Problem-Solving Exercises: 19

Answer

$\sqrt 105$

Work Step by Step

The Pythagorean Theorem says that $(leg_{1}) ^{2}$+$(leg_{2})^{2}$=$hypotenuse^{2}$. This formula is more commonly referred to as $a^{2}$+$b^{2}$=$c^{2}$ You are given the lengths of one leg as 16 and the length of the hypotenuse as 19. Substitute 16 in for a and 19 in for c. $a^{2}$+$b^{2}$=$c^{2}$ $16^{2}$+$b^{2}$=$19^{2}$ 256+$b^{2}$=361 Subtract 256 from both sides. $b^{2}$=105 Take the square root of both sides to find the length of the missing side. b=$\sqrt 105$
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