<image>At a certain moment, there is a passenger ship at sea point P, and lighthouse A is measured in the direction 30.0 north by east of P, and is 50.0 nautical miles away. The passenger ship sails at the speed of 60.0 nautical mile/hour in the direction of 60.0 from north by west for $\frac{2.0}{3.0}$hours to reach point B, then tan∠BAP = ()