Page 4 of 7

## 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: |

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 N_{A} 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 |