<image>At 9.0 in the morning, a ship departs from point A and sails in the direction due east at a speed of 40.0 nautical miles per hour, and arrives at point B at 9.0 and 30.0 minutes. As shown in the figure, the island M is measured from A and B. In the direction of 45.0 north by east and 15.0 north by east, then the distance between B and island M is ()