The resultant vector is the sum of the two velocity vectors.
[tex] \left[\begin{array}{ccc}-30\\12\end{array}\right] + \left[\begin{array}{ccc}2\\-4\end{array}\right] = \left[\begin{array}{ccc}-28\\8\end{array}\right] [/tex]
The attached picture (not to scale) shows the position of the resultant vector. You want to know the angle θ. In the right triangle,
[tex] \tan(\theta) = \frac{8}{28} \\
\theta = \arctan{\frac{8}{28}} \\
\theta = 16^\circ \quad (rounded) [/tex]
The boats's heading is 16 degrees north of west.
