She's approximately 361 m from the boat. Since she turned 120 degrees and swimmed for 400 m, she went back a vertical distance of 400*1/2=200 m, so she's 300-200=100 m away vertically. Horizontally, her distance to the boat is 400*cos30=200*\sqrt(3) meters, and using pythagoren's theorem, the distance to the boat is 100*\sqrt(13)=361m. Arctan (200*\sqrt(3)/100)=74 degrees, so she has to swim to south from west 90-74=16 degrees.
