Vector situation

Well, first of all you should see that 3.4 is an absurd result because it's less than the time it would take if there was no wind, and in fact there's wind blowing to the east which is not helping to the trajectory whatsoever.
I guess your problem with the triangle was that you were assuming it to be a triangle rectangle?

 

You're on the right track to use a triangle, but you've set it up incorrectly as your demonstrator said. If wind is blowing east, the airplane must point itself into the oncoming wind to cancel out its eastward force, resulting in a single vector pointing straight toward north. If you draw this triangle, you see the airplane's velocity is actually the hypotenuse and is not a leg of the triangle.