A boat starts out at 20km/h in direction 30 degrees. However, the boat is blown off course by a 12km/h wind blowing from 80 degrees. What direction does the boat now travel in and how far does it travel in one hour?

Answer 1

I wish the math people would stay away from navigation. They are hopeless at distinguishing between bearing and heading and here they evidently think a boat moves with the wind like an airplane forgetting that the hull is in the water sort of like a car on a road in a crosswind slipping sideways a bit but not traveling sideways at the wind speed.
But anyway making their nutty assumption and assuming angles are clockwise from north:
speed east = 20 sin 30 - 12 sin 80
speed north = 20 cos 30 -12 cos 80
so
speed east = -1.82
speed north = 15.2
Tan Angle from north = -1.82 /15.2
so angle = -6.83

compass direction clockwise from north = 360 -6.83 = 353

speed = distance/hour
= sqrt(1.82^2+15.2^2) = 15.3 km/hour