Known values: Angles a and c, Reference points A, B and C coordinates (Tienstra’s Method).
Solution: Station P coordinates.
1. Calculate baselines AB, BC and CA bearing angles.
Checking the sign value of all subtractions Dx and Dy above, the bearing angles of lines AB, BC and CA are calculated referencing the table below:
2. Calculating angles A, B and C of the three coordinated reference points respectively:
Always add angles A, B and C for checking calculations: A + B + C = 200g
3. Checking on the "danger circle" observations error, thus estimating on whether all four points lie on (or sufficiently close to) the circumference of a circle or a straight line, which would lead to no or high risk of an erroneous solution.
4. Calculating coefficients K1, K2 and K3
5. Calculating station’s P coordinates:
6. Validating results: