Assume the following fact: If an airplane flies with velocity V(a) relative to the air and the velocity of the wind is W then the velocity vector of the plane relative to the ground is V(g) = W + V(a).
Now suppose that the Wind is blowing from the North-East at 50 mi/h and that the pilot wishes to fly due East at 500 mi/h. What should the plane's apparent velocity vector V(a) be?
My issue with this problem, isn't that I didn't get an answer at all, I got a vector of magnitude 537 approximately which is correct, but I got an angle of around 4 degrees but the text book says that its 86 degrees. I can't find where I went wrong in that calculation. Any help you can offer will be greatly appreciated.
Notice that the coordinate system has the zero angle in the North direction. Going to East is at $90^\circ$. My guess is that you calculated that you have $4^\circ$ angle with respect to the East direction. The angle with respect to North is $90^\circ-4^\circ=86^\circ$