Bow-and-beam bearings

Bow-and-beam bearings are a running-fix special case that gives distance off a fixed object using the four-point rule. The navigator notes the time when the object lies 045 degrees on the bow, the four-point bearing, then again when it is abeam at 090 degrees relative. Because the two relative bearings and the run between them form an isosceles right triangle, the distance run between the two observations equals the distance the object is abeam, with no trigonometric tables needed. It assumes steady course and speed and no current. The result fixes the ship’s position abeam of the mark.