Now, let's do a simple problem in grant boundary adjustment. The sketch shows the record, retracement, and tie. First calculate the bearing and length of the record connecting line and the control connecting line. The legs of the right triangles trace the actual latitude and departure of the record line, North 59.20, East 21.55, North 34.71, East 41.37. Then, the tie to the identified corner 4 chains Southeast, 22 degrees, gives us the true latitude and departure of the control line, North 90.20, East 64.42.

Using the reduced cardinal equivalents we can apply trig ratios for tangents to determine the bearings of the record and control line.