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 114: 67


The circumference of the earth is 24,800 miles

Work Step by Step

We can convert the angle to radians: $\theta = 7^{\circ}12'$ $\theta = (7+\frac{12}{60})^{\circ}$ $\theta = (7.2^{\circ})(\frac{\pi~rad}{180^{\circ}}) = 0.1257~rad$ We can find the earth's radius: $S = \theta ~r$ $r = \frac{S}{\theta}$ $r = \frac{496~mi}{0.1257~rad}$ $r = 3945.9~mi$ We can find the circumference $C$ of the earth: $C = 2\pi~r$ $C = (2\pi)(3945.9~mi)$ $C = 24,800~mi$ The circumference of the earth is 24,800 miles
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