CJam -41 -40 -39 -38/35 31/26
This seems to work. It is my first attempt at CJam and/or codegolf. Run the code at http://cjam.aditsu.net/. In the section called input just place the variables as integers delimited with spaces in the input block in this order: distance D, landmark x, starting x, landmark y, starting y (for example 20 10 5 10 5). I had posted a previous one based on a misunderstanding of the equation that has been resolved. I also had been returning answers as probability ratios rather than percentages. Note: the second code has only 31 characters but combines alot from another user's CJam code.
Accuratish one without arcsine being directly called (44 characters):
ririri- 2#riri- 2#+ .5#/:A1<AA3#6/+P/1?100*
Even more accurate (52 characters):
ririri- 2#riri- 2#+ .5#/:A1<AA3#6/+A5#40/3*+P/1?100
The absolute best I've written is 26 characters. I've still learned alot by watching professorfish's attempts but the crux is mine. I assumes (potentially incorrectly) that if you can see the landmark if it is closer (not closer than or equal to) your sight radius.