Trigonometry (10th Edition)

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

Chapter 3 - Radian Measure and the Unit Circle - Section 3.2 Applications of Radian Measure - 3.2 Exercises - Page 104: 25

Answer

$44^{\mathrm{o}}$ N

Work Step by Step

Arc length s (for central angle $\theta$):$ \quad s=r\theta$, where $\theta$ is in radians Converting between Degrees and Radians 1. Multiply a degree measure by $\displaystyle \frac{\pi}{180}$ radian and simplify to convert to radians. 2. Multiply a radian measure by $\displaystyle \frac{180^{\mathrm{o}}}{\pi}$ and simplify to convert to degrees. ---------------- $r=6400$ km, $s=1200$ km $ s=r\theta,\ \quad$ ... solve for $\theta$ $ 1200=6400\theta$ $\displaystyle \theta=\frac{1200}{6400}=\frac{3}{16}$ see case 2 of converting .... $\displaystyle \theta=\frac{3}{16}\cdot\frac{180^{\mathrm{o}}}{\pi}\approx$10.7429586587$\approx 11^{o}$ The north-south angle between the two cities is about $11^{0}.$ South Dakota is north of Texas, Madison has the greater latitude The latitude of Madison is $x=$ (Dallas:$33^{o}$) + $11^{\mathrm{o}}$ The latimde of Madison is $44^{\mathrm{o}}$ N.
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