Kirk and Rose have misread their maps while on a hiking date. After walking around aimlessly for three hours they finally come upon a ranger station. It is on the opposite side of a river whose straight banks are $150$ feet apart. The good news is that there is a small motor boat tied to a dock with a call box on their side of the river. They phone the ranger station and learn: $(1)$ the river current flows parallel to its banks, and its speed at any point$$x$$feet from either bank is $6$sin$(($pi$/150)$x$)$ feet per second; $(2)$ the boat travels at a constant rate of $5$ feet per second in still water. They also receive some bad news: $(1)$ the boat has a broken rudder and can only head in a fixed direction; $(2)$ the land is infested with poisonous snakes on the ranger station side of the river, so they must head off at an angle that results in their arriving exactly at the dock in front of the ranger station.$$So at what angle should they set off to arrive at the ranger station.$$