What an amusing problem! Now it seems to be easy - in contrast to prima facie :^) Special thanks to Vorokh Sergey and Mamonov Anton, who proved correctness of my solution.

And some test data

input #1:
0 0 90 5
5 4.9
output #1:
28.2176

input #2:
0 0 90 5
0 -0.000001
output #2:
31.4159

Can you explain the answer to the input#1?