Chapter 14.2, Problem 2ST

To determine

To find: The value of true course bearing.

Answer to Problem 2ST

The value of true course bearing is $23.8°$ .

Explanation of Solution

Given:

The speed of the current to the south is $15\text{km}/\text{hr}$ .

The course has the heading of $130°$ at the speed of $20\text{km}/\text{hr}$ .

Calculation:

Consider heading bearing is $\alpha =130$ .

Then, by the law of cosines,

  $\begin{array}{l}{w}^2={15}^2+{20}^2-2\left(15\right)\left(20\right)\cos 130°\\ w=38\end{array}$

Then, by the law of sin.

  $\begin{array}{l}\frac{\sin \theta }{20}=\frac{\sin 130}{38}\\ \sin \theta =0.403\\ \theta =23.8°\end{array}$