Azimuth closure at an azimuth check point for a third-order geodetic network, class I is given by which formula?

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

Answer: (D)

Azimuth checks quantify how consistent measured directions are in a network. The small random errors in angular observations accumulate, but since they are independent, the total closure grows with the square root of how many azimuths are involved. So we express the allowable azimuth closure as a simple scaling: ΔA ≤ k √N, with ΔA in arc seconds, N the number of azimuth observations, and k a constant that depends on the network’s order and class.

For a third-order geodetic network of class I, the standard value for k is 10.0. That means the maximum permissible azimuth closure at an azimuth check point is 10 times the square root of N, in arc seconds. This choice reflects the expected precision and error behavior for this network type; the other constants would be used for different orders or classes, where the allowable closure would be smaller or larger accordingly. For example, with 25 azimuths, the limit would be 10√25 = 50 arc seconds.