Chapter 4.8, Problem 37E

To determine

To find: the bearing should the captain take.

Answer to Problem 37E

Angle of bearing that should be taken by the captain to sail directly to the port will be

  $\text{N}36.7°\text{W}$ .

Explanation of Solution

Given information:

A ship is 45 miles east and 30 miles south of port. The captain wants to sail directly to port.

Calculation:

Let us consider a ship at point $S$ which is 45 miles east and 30 miles south to port as shown in the figure,

Let angle of bearing directly from $S$ to $P$ be $\theta$ .

In the figure $\angle NSW=\angle ESP=\theta$

Now consider right $\Delta SRP$ , right angled at $R$ , using the fact that

  $\begin{array}{c}\tan \theta =\frac{30}{40}\\ \tan \theta =0.66\\ \theta =\arctan 0.66\\ \theta =36.7°\end{array}$

And since, $\angle NSW=\angle ESP=\theta$

Angle of bearing that should be taken by the captain to sail directly to the port will be

  $\text{N}36.7°\text{W}$