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3. Azimuth


 
Figure F-2
Azimuth Observation 

Equation F-4 is the angle of a line from the meridian in terms of a its coordinates.

  Equation F-4

A: At point
T: To point
αAT: angle from meridian
QAT: quadrant addend

The angle from the meridian can be to the right (+) or to left (-) depending on the coordinate differences signs. This places the angle in one of the four quadrants, Figure F-3.

 
Figure F-3
Angle from Meridian 

The value of QAT, added to the angle to obtain the azimuth, depends on the quadrant. Table F-1 shows the sign of α, its quadrant and QAT value.

Table F-1
Azimuth for a Line ij by Quadrant
 

Partial derivatives of Equation F-4 are taken with respect to each coordinate of both points. The partial derivative for NF is:

 

Remaining partial derivatives are:

Equation F-5 is the azimuth observation equation, evaluated at initial coordinate approximations.

  Equation F-5 
Equation F-6