Calculation example – Re-establishing an accessible Reference Station

Re-establish the reference station T (accessible by the surveyor) onto position B and calculate the coordinates of stations A and B.

A second reference station P is far but visible from T. By occupying reference station T, measure angles τ’ and θ. From station B, measure angle β’ and from station A, measure angle α’. Finally, measure distance (BA).

1. Angle measurements include uncertainties, causing inaccurate result on the sum of triangle angles.

τ' +β' '+α' -200gon= w

Equally distribute discrepancy w and correct values for all angles measured:

and

τ+β+α=200gon

2. By applying the Second Fundamental Surveying Problem and the known coordinates of reference stations T and P, calculate the bearing angle TP:

Then, calculate bearing angles TB and TA:

4. Considering the known coordinates of reference station T and applying the equations of the First Fundamental Surveying Problem: