Assume a 2D plane and both the birds start at origin. +X is east, -X is west, +Y is North, -Y is South.
So, after travel position of bird1 is (-2.8, 2.7) and bird2 is (-2.7,2.8);
slope of bird1 is 2.8/2.7
slope of bird2 is 2.7/2/8
Now we have two solpes b1 and b2
formula = (b2-b1)/(1+b1*b2);