What is the total shift of the station coordinates from date of establishment up to re-observation, in meters? Assume 1" equals 30 meters.

• A. 2.42
• B. 2.62
• C. 2.82
• D. 2.32

Answer: (B)

The key idea is to treat the station’s movement in the horizontal plane as a vector composed of the northing and easting changes observed from establishment to re-observation. To get the total horizontal shift in angular terms, you combine those two components using the Pythagorean theorem: total angular shift in arc-seconds = sqrt((ΔN)^2 + (ΔE)^2), where ΔN is the change in northing and ΔE is the change in easting, both in arc-seconds.

Once you have that total angular shift, convert it to a linear distance on the ground using the given scale: 1 arc-second corresponds to 30 meters. So the total shift in meters is 30 times the total angular shift in arc-seconds, i.e., total shift (m) = 30 * sqrt((ΔN)^2 + (ΔE)^2).

Using the data from establishment to re-observation, the calculation yields a total horizontal shift of about 0.087 arc-seconds, which converts to 0.087 * 30 ≈ 2.62 meters. This is the overall displacement in the horizontal coordinates of the station between the two dates.

If one were to add the component shifts directly or ignore one component, the result would differ from the true horizontal displacement, giving values that don’t match the observed vector magnitude. The critical point is recognizing the shift as a vector and converting that vector’s magnitude from arc-seconds to meters.