Start the Triangle Solver app; press Shift-Clear to blank out any values that might be there; set the angle mode to degrees and enter 5,4,3 for a, b & c respectively. Press Solve and see angle A=90. So far so good.
Now press the Degree soft menu and then Radians. The A=90 has now changed to 89.9999999997. I wouldn't normally worry too much about such things but the HP39gII gets it right i.e. returns to 90. :-)