E. Example Intersections
Two different intersection types are solved using triangle and arcbased methods to demonstrate the different computation process. Additional decimal places will be carried in computations to minimize rounding errors.
1. Distancedistance
Given the information on the diagram, determine the coordinates of point 101.


Figure E1 
Step (1) For both methods is to inverse along the base line 3020
a. Trianglebased 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. Arcbased method
Step (2) Set up and solve Equations D6 through D9.
Step (3) Use Equations D10 and D11 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.
Point  North  East  From base line 
101_{1}  5077.015  1363.991  north east 
101_{2}  4574.617  1085.956  south west 
The correct intersection point is 101_{2}: (4754.617 ft N, 1085.956 ft E), same as the trianglebased solution.