Q. 114 - Precalculus Enhanced with Graphing Utilities

Question

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.

Step-by-Step Solution

Answer

The length of the arc is 1.15 mi

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 $s=r\theta$

$$\begin{gathered} s=3960mi\left(1\text{'}\right) \\ s=3960mi\left(1\text{'}\frac{1^o}{60\text{'}}\frac{\mathrm{\pi }}{{180}^{\circ }}\right) \\ s=\frac{11\mathrm{\pi }}{30}=1.15mi \end{gathered}$$