Calculate the coordinates of a distant point Tn, referencing measured angles and coordinates of four known points.
Known values: Coordinates of points T1 (X1, Y1), T2 (X2, Y2), T3 (X3, Y3) and T4 (X4, Y4). Angles α’ and β’.
T1 : Χ1 = 1234,48m T2 : X2 = 2125,78m
Y1 = 4723,20m Y2 = 3951,11m
T3 : X3 = 5112,84m T4 : X4 = 7215,46m
Y3 = 3874,25m Y4 = 4630,24m
α’ = 83,1381g β’ = 90,2465g
Solution: Coordinates of point Tn (Xn, Yn).
Angles α and β cannot be measured due to obstructed visibility between point T2 and T3.
For calculating angles α and β, apply the 3rd Fundamental problem.
First, calculate bearing angles G23 and G34.
G23 = G12 + (β+β’) + 200 – k*400 (1)
G34 = G23 + (α+α’) + 200 – k*400 (2)
where k integer so that the numeric expression preceding k*400 decreases as many times so the Bearing angle numeric result stands between 0 and 400 grads.
By replacing in (1) and (2):
Calculate angle γ from triangle T2T3Tn:
Applying sine law:
Applying the 1st Fundamental problem to calculate the coordinates of point Tn:
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