An airplane needs to head due north, but there is a wind blowing from the southwest at 58 km/hr. The plane flies with an airspeed of 546 km/hr. To end up flying due north, how many degrees west of north will the pilot need to fly the plane

4.3° west of north

Step-by-step explanation:

The wind is blowing toward a direction 45° east of north, so will have an easterly component that is ...

(58 kph) sin (45°) = 41.0122 kph

We want the easterly component of the airplane's flight to be the opposite of this, so the angle (x) east of north is ...

(546 kph) sin (x) = - 41.0122

sin (x) = - 41.0122/546

x = arcsin (-41.0122/546) ≈ - 4.31°

The pilot needs to fly 4.3° west of north to maintain a ground path that is straight north.