At 12:00 noon, a tugboat leaves the terminal on a heading North 15° to the West at a speed of 25 km/h. At the same time, a cruise ship leaves the terminal travelling at 80 km/h on a heading East 30º to the North.
Make a sketch using the axes provided and then find how far apart are the boats at two o’clock in the afternoon.
In 2 hours, the ships have gone 50 and 160 km
The angle between their headings is 75º
So use the law of cosines to find the desired distance x:
x^2 = 50^2 + 160^2 - 2*50*160 cos75º
x = 154.8 km