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: 22

Answer

14.1 ft

Work Step by Step

The ladder against the house forms a right triangle against the ground. The Pythagorean Theorem says that $(leg_{1}) ^{2}$+$(leg_{2})^{2}$=$hypotenuse^{2}$. This formula is more commonly referred to as $a^{2}$+$b^{2}$=$c^{2}$ The ladder forms the hypotenuse and the distance of the base from the house forms a leg of a right triangle. You are given the lengths of one leg as 5 and the length of the hypotenuse as 15. Substitute 5 in for a and 15 in for c. $a^{2}$+$b^{2}$=$c^{2}$ $5^{2}$+$b^{2}$=$15^{2}$ 25+$b^{2}$=225 Subtract 25 from both sides. $b^{2}$=200 Take the square root of both sides to find the length of the missing side. b=10$\sqrt 2$=14.1
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