An airplane pilot wishes to fly to his destination 500 mi due west, but the wind is blowing at 37.5 mi/hr toward 14.7° north of west. The speed of the plane relative to the air is 159.3 mi/hr. At what angle (south of west) must the pilot orient the plane in order to fly to his destination directly?
If the pilot orients the plane at that angle, what will be the speed of the plane relative to the ground?