Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 3 - Section 3.4 - Arc Length and Area of a Sector - 3.4 Problem Set - Page 153: 15

Answer

5.03 cm

Work Step by Step

Radius $r=1.2\,cm$ In order to complete $360^{\circ}$ the minute hand takes 60 minutes. Therefore in 40 minutes it covers an angle of $360^{\circ}\times\frac{40}{60}=240^{\circ}$. That is, central angle $\theta=240^{\circ}=(240\times\frac{\pi}{180})\,radians=\frac{4\pi}{3}\,rad$ Arc length $s=r\times\theta=1.2\,cm\times\frac{4\pi}{3}=5.03\,cm$
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