I'm having trouble figuring this out. An airplane has an airspeed of 160 mph. It is to make a flight in a direction of 80° while there's a 20 mph wind from 310°. What will the airplane's actual heading be?

I'd appreciate any help especially on how you determined what angles to use. Thank you.

1 answer

just convert everything to x-y values, add them up, and change back to headings. If his heading is θ, then we need

160sinθ - 20sin310° = v*sin80°
160cosθ - 20cos310° = v*cos80°

solve that and you get
θ = 74.5°
v = 172.1

makes sense, since the wind is blowing to the SE, adding to his speed.