Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 10 - Geometry - 10.6 Right Triangle Trigonometry - Exercise Set 10.6: 15

Answer

$b \approx 22$ yd

Work Step by Step

RECALL: In a right triangle, $\sin{A} = \dfrac{\text{length of opposite side}}{\text{length of hypotenuse}} \\\cos{A} = \dfrac{\text{length of adjacent side}}{\text{length of hypotenuse}} \\\tan{A} = \dfrac{\text{length of opposite side}}{\text{length of adjacent side}}$ Use the tangent formula to obtain: $\tan{A} = \dfrac{\text{length of opposite side}}{\text{length of adjacent aide}} \\\tan{33^o}=\dfrac{14}{b}$ Multiply $b$ to both sides of the equation to obtain: $b \cdot \tan{33^o} = 14$ Divide $\tan{33^o}$ on both sides of the equation to obtain: $b = \dfrac{14}{\tan{33^o}} \\b = 21.55810949 \\b \approx 22$ Thus, $b \approx 22$ yd.
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