Question

A plane intends to north with a speed of 250 m/s relative to the ground through a high altitude cross wind of 50 m/s coming from the east. Determine the bearing that the plane should take( relative to due north),
A) the planes speed with respect to the air answer

Answer 1

The plane takes a heading, not a bearing.
So, draw the velocity triangle. You should be able to see that

speed: s = √(250^2+50^2)
heading: tanθ = 50/250

Answer 2

101