Chapter 14, Problem 1CR

To determine

To find:The actual heading of the ship.

Answer to Problem 1CR

The actual heading of the ship is $177.3°$ .

Explanation of Solution

Consider the figure shown below.

  

Figure (1)

The ground speed of the plane is calculated as,

  $\begin{array}{c}{\left|\left|x\right|\right|}^2={25}^2+6^2-2\left(25\right)\left(6\right)\cos 152°\\ =925.9\\ \left|\left|x\right|\right|\approx 30\end{array}$

The bearing of x is $172°+\theta$

The value of $\theta$ is calculated as,

  $\begin{array}{c}\frac{\sin \theta }{6}=\frac{\sin 152°}{30}\\ \theta \approx 5.3°\end{array}$

The actual heading of the ship is,

  $\begin{array}{c}\text{Actual}\text{heading}=172°+\theta \\ =172°+5.3°\\ =177.3°\end{array}$

Therefore, the actual heading of the ship is $177.3°$ .