Azimuth closure at an azimuth check point for a first-order geodetic network is given by which formula?

• A. 1.7√N
• B. 3.0√N
• C. 4.5√N
• D. 10.0√N

Answer: (A)

In a first-order geodetic network, angular misclosures are treated statistically, so the allowable azimuth error at an azimuth check point grows with the square root of how many azimuths are involved. This reflects how random measurement errors accumulate like a random walk: the combined effect does not grow linearly with N, but with sqrt(N).

For first-order networks, the conventional tolerance is about 1.7 arc-seconds per sqrt(N). Therefore the azimuth closure limit is 1.7√N arc-seconds. This keeps the angular integrity tight as more measurements are added. The larger coefficients (3.0, 4.5, 10.0) correspond to looser tolerances used in less demanding networks, which is why they’re not the appropriate standard here.