I would strongly recommend against pouring any concrete or doing any other permanent work based on any mathematical answer you get.   There are a whole lot of ways for the auger not to conform to the equation unless you create the equation basically by setting up the auger and getting a bunch of actual measurements, in which case you may as well just measure the distance you need to know and skip the equation. 

First problem, auger manufacturers don't seem to have very acurate tape measures.  Their augers may or may not be the length advertised.  Second problem, the undercarriage of the auger may interfere with setting it up where it "should" be.  Third problem, the bottom of the auger will be an unspecified distance from the ground.  Fourth problem, the top of the auger  will be an unspecified distance from the top of the bin, both vertically as well as possibly laterally.  Fifth problem, I wouldn't pour concrete based on "say, 40' high"

Go set the auger up and mark it out, like was suggested.  That way there isn't much room for things to go wrong.