law of cosines will get it quickly ...
A plane flying due east at 200 km/hour encounters as a 40 km/hour north-easterly wind. The resultant velocity of the plane is the vector sum v = v1 + v2, where v1 is the velocity vector of the plane and v2 is the velocity vector of the wind. The angle between both vectors is pi/4. Determine the resultant speed of the plane (the length of v).
I don't like vectors. Maybe they don't like me either.
Dang, this whole chapters on vectors. =(
I miss integrals.