Known values: Angles α, β and θ – Distance (ΑΒ) – Coordinates (XT, YT) and (XP, YP).
Solution: Coordinates (XA, YA) and (XB, YB)
A second reference station P is far but visible from T and B. By occupying station A, measure angle α. From station B, measure angles β and θ. Finally, measure distance SAB.
1. By applying the Second Fundamental Surveying Problem and the known coordinates of reference stations T and P, calculate the bearing angle TP and distance STP:
2. By applying the sine law on triangle TAB, calculate the auxiliary distances STA and STB:
3. By applying the sine law on triangle TΡΒ, calculate angle ω:
4. Then, calculate bearing angles αTA and αTB:
5. Considering the known coordinates of reference station T and applying the equations of the First Fundamental Surveying Problem:
6. For validating the results, apply the following: