Chapter 12, Problem 18PT

To determine

To find: Length of the nautical mile.

Answer to Problem 18PT

Length of 1 nautical mile $=l=6092.5$ feet

Explanation of Solution

Given information:

  $1$ nautical mile $=l=6077-31\cos 2\theta$ feet

  $\theta ={120}^0$

Given

  $1$ nautical mile $=6077-31\cos 2\theta$ feet

On substituting

  $\theta ={120}^0$

We get

  $\begin{array}{l}l=6077-31\cos 2\theta \\ \Rightarrow l=6077-31\cos 2\left({120}^0\right)\\ \Rightarrow l=6077-31\cos \left({240}^0\right)\\ \Rightarrow l=6077-31\left(-0.5\right)\\ \Rightarrow l=6077+15.5\\ \Rightarrow l=6092.5\end{array}$

Therefore,

Length of 1 nautical mile $=l=6092.5$ feet