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 - Page 498: 55


The distance of the base of the ladder from the wall is about $4$ $ft.$

Work Step by Step

From the diagram, the ladder leaning against a building forms a right triangle. We can use the Pythagorean theorem to figure out how far away the base of the ladder is from the building. The Pythagorean theorem is given by the formula $a^2 + b^2 = c^2$, where $a$ and $b$ are the legs of the right triangle and $c$ is the hypotenuse. Let's plug in what we know into the Pythagorean theorem: $15.5^2 + b^2 = 16^2$ Evaluate the exponents: $240.25 + b^2 = 256$ Subtract $240.25$ from each side of the equation to move constants to the right side of the equation: $b^2 = 15.75$ Take the positive square root to solve for $b$: $b \approx 4$ The distance of the base of the ladder from the wall is about $4$ $ft.$
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