E. Example Intersections

Two different intersection types are solved using triangle- and arc-based methods to demonstrate the different computation process. Additional decimal places will be carried in computations to minimize rounding errors.

1. Distance-distance

Step (1) For both methods is to inverse along the base line 30-20

a. Triangle-based method

Step (2) Compute angle at 30 by Law of Cosines.
Step (3) Compute direction from 30 to 101.
Step (4) Perform a forward computation from 30 to 101.

Math Check: Compute coordinates from 20.

Step (1) Compute angle at 20 by Law of Sines.
Step (2) Compute direction from 20 to 101.
Step (3) Perform a forward computation from 20 to 101. Both coordinates check.

b. Arc-based method

Step (2) Set up and solve Equations D-6 through D-9.

Step (3) Use Equations D-10 and D-11 to compute the two intersection points

Step (4) Of the two, select the appropriate intersection point.

Point 101 is located southwest of the base line.

The correct intersection point is 101₂: (4754.617 ft N, 1085.956 ft E), same as the triangle-based solution.