An airplane flies at airspeed (relative to the air) of 430 km/h . The pilot wishes to fly due North (relative to the ground) but there is a 43 km/h wind blowing Southwest (direction 225◦).

Question

In what direction should the pilot head the plane (measured clockwise from North)?
Answer in units of degrees.

Answer 1

43/√2 = 30.4, so the wind's vector is (-30.4,-30.4)

If the plane flies on heading θ,

(-30.4,-30.4)+(430cos(θ-45°),430sin(θ-45°)) = (0,y)

so, we have -30.4 + 430cos(θ-45) = 0
cos(θ-45) = 30.4/430 = 4.05

so, the plane flies N41°E

Answer 2

is 41 degrees east of north the exact degree number??? because a computer program wants the exact number and i cant round over or under 1%...