Programming Challenge: a classic trigonometry problem

[RMollov]

Isn't that the beauty of calculators like the HP48? I got the answer in a couple of minutes, while the pen and paper method did not seem to work for me cause I'm not that bright. It's a bit like " God made man, but Samuel Colt made them equal". :-)
Very interesting task, I'm looking forward to see some smart solutions to it. Thanks,