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b. Inverse Computation

An inverse computation is used to determine the distance and direction between two coordinate pairs. The computations involved are basically the same as those for determining a line's new length and direction from its adjusted lats and deps.

For the traverse shown in Figure F-7, how would we determine the length and direction of the line from point T to point R?

Figure F-7
Length and Direction Between Nonadjacent Points


Knowing the coordinates of the two points, we can determine the latitude and departure of the line from the coordinate differences, Figure F-8.


Figure F-8
Length and Direction from Coordinates


img20        Equation F-4


Note that the differences are the To point values minus the From point values.

img21        Equation F-5
img22   Equation F-6
-90° ≤ ß ≤ 90°    


The mathematic signs on the coordinate differences determine the direction quadrant, Figure F-9.

img14 2
Figure F-9
Converting ß to a Direction

If X and Y coordinates are used, remember that Y corresponds to N and X corresponds to E.