A Different Trigonometry Problem

It is perhaps fitting that this issue should discuss a problem that is half a century old. Take your mind back to the days before there was anything like a modern calculator or computer. What I want to discuss is a truly original problem in trigonometry. It is a problem in an applied setting, but it is not a modeling problem, because I was never told what the real world situation actually was. Probably I had no need to know.

I remember that there was an airborne computer involved, and that the weight and complexity of the computer were a big issue. The angles involved were relatively small. I originally thought that it mattered if they were in the first quadrant, but it really didn't.