Vanguard, the AOB calculated is from your initial observation. Add the number of degrees he's moved across your field of view to arrive at a final AOB (ie, add the bearing change to the AOB). At least, I believe that's your trouble...
Final AOB = calculated AOB + bearing change
Also, yes, it looks like the explanation was flipped like Powerthighs stated. The equation should have you subtracting (2 * cos bearing change * range 1 * range 2) from (range1 squared + range2 squared)... or the whole equation:
c^2 = a^2 + b^2 - 2 * a * b * cos C
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