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Q. 114

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Found in: Page 367

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# Nautical Miles A nautical mile equals the length of arc subtended by a central angle of 1 minute on a great circle† on the surface of Earth. See the figure. If the radius of Earth is taken as 3960 miles, express 1 nautical mile in terms of ordinary, or statute, miles.

The length of the arc is 1.15 mi

See the step by step solution

## Step 1. Given Information

The problem asks to find the length of the arc $s,$ if the radius of the earth is taken as 3960 miles, expressing 1 nautical mile in terms of ordinary, or statue, miles. Hence,

1 nautical mile$=$the length of the arc, subtended by a central angle, $\theta$ of 1 minute on a great circle on the surface of the earth.

## Step 2. Finding the length of the arc

Using formula $s=r\theta$

$s=3960mi\left(1\text{'}\right)\phantom{\rule{0ex}{0ex}}s=3960mi\left(1\text{'}\frac{{1}^{ο}}{60\text{'}}\frac{\mathrm{\pi }}{{180}^{\circ }}\right)\phantom{\rule{0ex}{0ex}}s=\frac{11\mathrm{\pi }}{30}=1.15mi$