NSolve takes an option WorkingPrecision which lets you specify the number of decimal places to work to. It may also make sense to control the input precision of the real number with, say, 33.677`50 to pad it to 50 decimal places.

You seem to be asking "If I have a circle with radius 10 centered at {-90, 27} what is its height at x=33.677. Put like that it should be pretty obvious that there will be no solution except for -100<x<80. Also having b2 in the answer suggests your code does not do say what you say it says. b2 is coming from somewhere. I suggest you post the code in its entirety.