Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 6 - 6.2 - Right Triangle Trigonometry - 6.2 Exercises - Page 442: 59


$r=\frac{64\sqrt 3}{3}$ $x=\frac{32\sqrt 3}{3}$

Work Step by Step

$sin~θ=\frac{opp}{hyp}$ $sin~60°=\frac{32}{r}$ $\frac{\sqrt 3}{2}=\frac{32}{r}$ $r=\frac{32}{\frac{\sqrt 3}{2}}=32\frac{2}{\sqrt 3}=\frac{64}{\sqrt 3}\frac{\sqrt 3}{\sqrt 3}=\frac{64\sqrt 3}{3}$ $tan~θ=\frac{opp}{adj}$ $tan~60°=\frac{32}{x}$ $\sqrt 3=\frac{32}{x}$ $x=\frac{32}{\sqrt 3}\frac{\sqrt 3}{\sqrt 3}=\frac{32\sqrt 3}{3}$
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