math
posted by Brian on .
A ferry boat operator is required to drive directly to the opposite side of the river (starting at south side of river is A and the north side of river is B where boat will end up) but does not know where to point the nose of the boat. The river is flowing due West at 4 mph and the boat can bravel 9 mph over still water. What direction (CW relative to N) should the ferry driver point the nose of the boat?

Draw a diagram. Draw your line straight north from A, and a line east from A of length 4. The hypotenuse is the speed of the boat, 9.
That is, for every 9 miles the boat travels in the desired direction, it will drift 4 miles west. ending up directly north of A.
So, the angle a, reckoning from the north direction is such that
sin(a) = 4/9 = .4444
so, a = N 26.4° E