I should point out that there I made a mistake, that is the angle the plane makes with the horizontal so the actual angle is .
When I drew my diagram I put the plane at the origin and drew a horizontal line right to represent the wind (100) and a vertical line up to represent the plane going north (450)
I then made a right-angled triangle from these lines with an angle \theta between them. Part a is asking for the hypotenuse which is Pythagoras' as you got.
Part b is one of the trig ratios, since the opposite and the adjacent are known directly I used .
However, this is the angle is makes with East (as I forgot in my last post), to find the answer from North we need to take this angle from 90.