Create a free account and view content that fits your specific interests in civil engineering __Learn More__

Contents [show]

**Calculate the coordinates of a distant point T _{n}, referencing measured angles and coordinates of four known points.**

**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

** **

Calculation example - Calculate the Bearing Angle of any Baseline of a Traverse Network (Third Fundamental Surveying Problem)Calculation example - Three Point ResectionGauss's Area Calculation FormulaCalculation example - Determine the water content within a soil sampleCalculation example - Determine the specific gravity of a soil grain GsCalculation example – Central projection and projective transformation of a planeCalculation example – The intersection methodCalculation example – Elevation Calculation along Profile TangentCalculation example – Elevation calculation and grade along a profile vertical curveCalculation example – Similarity Transformation in 2-D spaceCalculation example – Volume Calculation – Ramp Reaching a Vertical WallCalculation example – Indirect length measurement with basic trigonometryCalculation example – Road design– Circular arc implementationCalculation example – Road design– Circular arc implementation 2Calculation example – Re-establishing an accessible Reference StationCalculation example – Re-establishing an inaccessible Reference StationCalculation example – Calculate the height of a buildingCalculation example – Calculate the height of a building - 2Calculation example - Calculate the height of an object when its base is inaccessibleCalculation example - Calculate the height of an object when its base is inaccessible #2Calculation example - Calculate the height of an object when its base is inaccessible #3Calculation example - Calculate the height of an object when its base is inaccessible #4Calculation example - Calculate the height of an object when its top and bottom are visible but inaccessibleCalculation example - Calculate the height of an object when its top and bottom are visible but inaccessible #2Calculation example - Calculate the height of an object from three angles of elevationCalculation example - Calculate inclined angle of a bendCalculation example - Find the coordinates of the intersection of two linesCalculation example - Find the coordinates of the intersection of two linesCalculation example - Seam true thickness and gradient calculationCalculation example - Find the apparent dip of a plane or seam in any directionCalculation example - Find the rate of full dip of a plane or seam, given its direction and the rate and direction of an apparent dipCalculation example - Find path gradients in different directions, given the rate and direction of full dipCalculation example - Find the bearing of an apparent dip (two symmetrical to full dip directions), given the rate and direction of full dipCalculation Examples

The Golden Gate Bridge opened on May 27, 193...

Given the rate and direction of full dip of a pla...

Given the rate and direction of full dip of a plan...