In a third order, class II geodetic control network, azimuth closure at an azimuth check point (seconds of arc) is equal to which expression?

In a third order, class II geodetic control network, azimuth closure at an azimuth check point (seconds of arc) is equal to which expression?

• A. 16
• B. 8 or 12
• C. 12√N
• D. 4

Answer: (C)

Think of angle observations as small random errors. When you sum many independent angular errors to form a closure around a network, the total misclosure grows with the square root of how many azimuths are involved. For a third-order, class II geodetic network, this statistical behavior is captured by the expression 12 times the square root of N, in seconds of arc. The factor 12 reflects the typical precision for azimuth observations in that class, while the √N term shows how the accumulated misclosure increases as you include more azimuths in the network. The other options don’t scale with the number of azimuths, so they don’t fit the standard expectation.

Think of angle observations as small random errors. When you sum many independent angular errors to form a closure around a network, the total misclosure grows with the square root of how many azimuths are involved. For a third-order, class II geodetic network, this statistical behavior is captured by the expression 12 times the square root of N, in seconds of arc. The factor 12 reflects the typical precision for azimuth observations in that class, while the √N term shows how the accumulated misclosure increases as you include more azimuths in the network. The other options don’t scale with the number of azimuths, so they don’t fit the standard expectation.