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 Test - Page 537: 19


$TU \approx 16.3$

Work Step by Step

First, we want to know what angle is opposite the side in question. The angle that is opposite to the side we are looking for is $\angle V$, so let's plug in what we know into the formula for the law of cosines: $(TU)^2 = 12^2 + 24^2 - 2(12)(24)$ cos $38^{\circ}$ Evaluate exponents first, according to order of operations: $(TU)^2 = 144 + 576 - 2(12)(24)$ cos $38^{\circ}$ Add to simplify on the right side of the equation: $(TU)^2 = 720 - 2(12)(24)$ cos $38^{\circ}$ Take the square root of both sides to solve: $TU \approx 16.3$
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