Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 3 - Radian Measure and the Unit Circle - Section 3.2 Applications of Radian Measure - 3.2 Exercises - Page 112: 44

Answer

0.12 mi

Work Step by Step

$2^{\circ}30'=2.5^{\circ}$ In radians, central angle $\theta=2.5^{\circ}\times\frac{\pi\,rad}{180^{\circ}}=0.04363323\,rad$ Considering the distance 2.7 mi as the radius($r$) and the length of the train as arc length($s$), we can find the length of the train using the relation $s=r\theta$. $s=2.7\,mi\times0.04363323\approx0.12\,mi$ (rounded off to 2 significant figures)
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