**Known values:** Coordinates of points T_{1} (X_{1}, Y_{1}), T_{2 }(X_{2}, Y_{2}), T_{3 }(X_{3}, Y_{3}) and T_{4 }(X_{4}, Y_{4}). Angles α’ and β’.

T_{1} : Χ1 = 1234,48m T_{2} : X2 = 2125,78m

Y1 = 4723,20m Y2 = 3951,11m

T_{3} : X3 = 5112,84m T_{4} : X4 = 7215,46m

Y3 = 3874,25m Y4 = 4630,24m

α’ = 83,1381g β’ = 90,2465g

**Solution:** Coordinates of point T_{n} (X_{n}, Y_{n}).

*Angles α** **and β** cannot be measured due to obstructed visibility between point T _{2} and T_{3}.*

For calculating angles α and β, apply the 3^{rd} Fundamental problem.

First, calculate bearing angles G_{23} and G_{34}.

G_{23} = G_{12} + (β+β’) + 200 – k*400 (1)

G_{34} = G_{23} + (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.

G_{12} calculation:

G_{23} calculation:

G_{34} calculation:

By replacing in (1) and (2):

And

Calculate angle γ from triangle T_{2}T_{3}T_{n}:

Applying sine law:

Applying the 1^{st} Fundamental problem to calculate the coordinates of point T_{n}:

And

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