Since the ship sailing 121 degrees, the ship is going North-west at an angle of 31 degrees from the vertical 'n' axis (this is determined by subtracting 90 from 121). With this information, we have a right triangle whose hypotenuse is 305 miles and one angle is 31 degrees. The distance south to the starting point is also one of the legs of the right-triangle. We can find this distance ('d'), from:

cos(31)=(d)/(305)

Solving for 'd', we get:

d=261.44 miles