Your calculated value could be 5% high or 5% low.
If h is 5% higher than the true height (H) of the building then
h = H + 0.05H
h = 1.05H
h/1.05 = H = 104.6657
If h is 5% lower than the true height of the building then
h = H - 0.05H
h = 0.95H
h/0.95 = H = 115.6832
The angle of elevation must be between:
Angle1: arctan (115.6832/40)
Angle2: arctan (104.6657/40)
The question is "How accurately must the angle be measured..."?
Determine half the difference be Angle1 & Angle2.
That is how accurately it must be made.
Most likely you are required to get the angle to the nearest tenth of a degree.
it could be plus or minus minutes of arc.