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Q. 114

Expert-verifiedFound in: Page 367

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

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.

Using formula $s=r\theta $

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

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