Island A is 190 miles from Island B. A ship travels 270 miles from Island A, but is off course 180 miles from Island B. What angle, in degrees must the ship turn in order to head straight for Island B?

Answer 1

Draw a diagram.
Consider A to be at (0,0)
B lies on the circle with center at (0,0) and radius 190
The ship ended up at a point P on a circle with center at (0,0) and radius 270, such that BP = 180
If we let B be due north of A, then the bearing of P from B is z degrees, where
cosz = 80/180
Now you can find the angle θ that the ship is off via
tanθ = 180sinz/270 = 2/3 sinz