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4. Horizontal Angle 

  
Figure F-4
Horizontal Angle Observation Examples

Equation F-7 is the horizontal angle observation equation in terms of point coordinates. 

  Equation F-7 

A: At point 
F: From point
T: To point
Az: Azimuth
α: angle from meridian
Q: quadrant addend

The horizontal angle is to the right and is the difference between azimuths from the At point (instrument location) to the To point (foresight) and From point (basksight). Equation F-7 is a combination of two Equations F-4: one for the foresight line, the other for the backsight.

Partial derivatives of Equation F-7 are taken with respect to each coordinate of all three points. The partial derivative for NA is: 

Remaining partial derivatives are:

Equation F-8 is the horizontal angle observation equation, evaluated at initial coordinate approximations.

  Equation F-8
Equation F-9