What is the difference between direction and angle? For example, "angle the man must steer his boat" vs. "direction the man must steer his boat". Are direction and angle the same in this case? Or does it mean I have to find the angle for both cases?
 A: It depends how you define the direction, but in general angle is a numerical measurement of direction.
For example, the direction could be east, north, west and south, or any combination of those such as north-east, south-west etc. Note that the direction does not need to be expressed via cardinal direction, it can be any literal description. But the angle must be a numerical value expressed relative to some direction, such as $45^\circ$ north-of-east, $60^\circ$ west-of-north etc.
A: Depends what you are asking.  Your sailor there could sail in the direction of a lighthouse (fixed point), or he might sail in the direction of another boat (moving target).
To steer at a particular angle, you still need a reference - either a compass point, or possibly at a fixed angle to the wind, which is important to a sailboat in a race, for example.
A: A sailor would  consider "direction" to be the magnetic compass direction (or gps reading); and possibly "angle" to be the angle between the boat's velocity vector and its center line (re. side slip).
