Surveying I– coordinate account

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Calculation of the horizontal angle from the coordinates

Figure 1. Horizontal angle α in the coordinate system

The angle α is the angle between the segments joining the points 2-0-1 with known coordinates. In surveying, we can determine the value of the horizontal angle α on the basis of previously calculated bearings* sides of the arms are looking for an angle:

α = A₀₁ – A₀₂

Is necessary to make a sketch (Figure 1.) With an indication of the angle α and angle β, which together constitute a round angle.

*If you do not remember how to calculate the bearing from coordinates of two points, click

Example

Calculate the value of the angle α is located between points 1, 0 and 2 (Figure 1).

Data:
0 ( 152,12m; 172,32m)
1 ( 237,63m; 357,78m)
2 ( 459,68m; 452,87m)

SOLUTION

Δx₀₁ = X₁ – X₀ = 85,51m
Δy₀₁ = Y₁ – Y₀ = 185,46m


φ₀₁ = arctg Δy₀₁ Δx₀₁


φ₀₁ = arctg 185,46 85,51


φ₀₁ = 72^g,49667

A₀₁ = 72^g,49667

Δx₀₂ = X₂ – X₀ = 307,56m
Δy₀₂ = Y₂ – Y₀ = 280,55m


φ₀₂ = arctg Δy₀₂ Δx₀₂


φ₀₂ = arctg 280,55 307,56


φ₀₂ = 47^g,07826

A₀₂ = 47^g,07826


α = A₀₁ – A₀₂ = 72^g,4967 – 47^g,0783 = 25^g,4184