Question

An airplane travels 209 km on a straight course making an angle of 22.5˚
east of due north. How far north and how far east does the plane travel
from its starting point?

Answer 1

The projection on the north direction is:

$$d_N = 209\cos22.5\degree \approx 193.1\space km$$

The projection on the east direction is:

$$d_E = -209\sin22.5\degree \approx -80.0\space km$$

Answer. 193.1 km, -80.0 km.