craigbeevers - if you're defining the angle as you do, then ideasrule is right. I looked at your post again and see you're defining it the same way as ideasrule. If you used cos, then you'd get a speed of over 300mph, which is clearly garbage!
I think you guys are making this problem harder than it needs to be! First off, determine the maximum speed the slower aircraft can accelerate to using the height advantage. If that's less that 210mph, then you don't need to worry about solving the PDEs.
Heres my thinking: