Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 3 - Review Exercises - Page 129: 26

Answer

$A=\frac{s^{2}}{2\theta}$

Work Step by Step

Step 1: $A=\frac{1}{2}r^{2}\theta$ Step 2: $A=\frac{1}{2}\times r\times r\times\theta$ Step 3: Since $s=r\times\theta$, $A=\frac{1}{2}\times r\times (r\times\theta)$ Step 4: $A=\frac{1}{2}\times r\times (s)$ Step 5: $A=\frac{1}{2}\times r\times (s)$ Step 6: Rearranging $s=r\theta$ as $r=\frac{s}{\theta}$ and substituting, $A=\frac{1}{2}\times \frac{s}{\theta}\times s$ Step 7: $A=\frac{s^{2}}{2\theta}$
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