[TheHound]

...and the "spread" of an angle is the square of the sine of the angle.

OK but how do you get the sine of the angle to square without trig - just wondering.

[VeritatisSplendor]

I'm telling you it's the square of the sine so you know what it is, but that's not the way the book develops it. Use the law of cosines instead -- cos C = (a^2 + b^2 - c^2)/2ab.

So, the "spread" of angle C can be defined in terms of the "quadrance" --

S(C) = 1-((Q(a)+Q(b)-Q(c))^2)/(4Q(a)Q(b))

I think the book has an even simpler formula, but the one I just showed follows immediately from the law of cosines, and the calculations don't require tables or calculators.