Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 8 - Applications of Trigonometric Functions - 8.1 Right Triangle Trigonometry; Applications - 8.1 Assess Your Understanding - Page 518: 1



Work Step by Step

The Pythagorean Theorem says that for a right triangle (if $z$ is the hypotenuse and $x,y$ are the other sides): $x^2+y^2=z^2$. Hence here if we denote the unknown length with $x$: $x^2+3^2=5^2\\ x^2+9=25\\ x^2=25-9\\ x^2=16\\ x=\pm\sqrt{16}\\ x=\pm4$ Since a side length is positive, then $x=4$.
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