Question

Island A is 190 miles from Island B. A ship travels 270 miles from Island A, but is off course and 180 miles from Island B. What angle, in degrees must the ship turn in order to head straight for Island B? (Hint: Remember, boats must turn from the front of the ship) (Need work to be shown) Thanks in advance!

Answer 1

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