In order to really understand what's going on here, you need some way to visualise it. I suggest drawing a pair of axes in order to comprehend what's going on.
Since the cruise ship travels 300 miles due east, this just means that the ship travelled 300 miles east. I recommend drawing a vertical line where he stops because we can more accurately understand what is going on. I have drawn the diagram that I think best represents this.
Now, based on the diagram, we want to find h, because that's the distance from our initial location to our final location.
Since 30 degrees is the outside angle, its supplement is 150 degrees.
Thus, we can now find h using the cosine rule.
[tex]h^{2} = 300^{2} + 175^{2} - 2(300)(175)cos(150)[/tex]
[tex]h^{2} = 90000 + 30625 - 105000 \cdot cos(150)[/tex]
[tex]h^{2} = 211,557.6674...[/tex]
[tex]h = 459.9953984...[/tex]
[tex]h \approx 459.995[/tex] miles.
Thus, the cruise ship is approximately 459.995 miles from its initial position.
