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 - Chapter Review - Page 535: 7


$x = 9\sqrt 3$

Work Step by Step

We can find the third side by using the Pythagorean theorem, which states that $a^2 + b^2 = c^2$, where $a$ and $b$ are the legs of the right triangle and $c$ is the hypotenuse. We are given the measure of one leg and the hypotenuse and are asked to find the other leg. Let's plug in what we know into the Pythagorean theorem: $9^2 + x^2 = 18^2$ Evaluate the exponents: $81 + x^2 = 324$ Add to simplify: $243 = x^2$ Rewrite $288$ as the product of a perfect square and another factor: $x^2 = 81 • 3$ Take the positive square root to solve for $x$: $x = 9\sqrt 3$
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