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 - Mid-Chapter Quiz - Page 515: 17


$x = 15.0$

Work Step by Step

Since we have the measure of one angle and the measure of the side opposite to that angle, we can use the tangent ratio to find $x$, which is the side adjacent to the given angle. The tangent ratio is given as follows: tan $A = \frac{opposite}{adjacent}$ Let's plug in what we know: tan $25 ^{\circ} = \frac{7}{x}$ Multiply each side by $x$: tan $25 ^{\circ}(x) = 7$ Divide both sides by tan $25^{\circ}$: $x$ = 7/tan $25 ^{\circ}$ Divide to solve: $x = 15.0$
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