# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Horizontal Angle and the Hand Bearing Compass**

**From:**Michael Dorl

**Date:**2011 Jun 04, 15:11 -0500

On 6/4/2011 1:38 PM, Greg Rudzinski wrote: > > Micheal Dorl wrote: > > " it would seem that the other angles would enter > into the solution. Surely there are other positions from which the > angle between A & B are the same but with different bearings." > > Every point on the arc of position will have the same difference > between the bearings to mark A and B. When determining the radius of > the circle half the distance between A and B is used so that two right > triangles are formed with the hypotenuse of each being the radius of > the circle. The half distance represents the opposite side so simple > trig will give you the Radius(hypotenuse) = 1/2 distance(opposite) A-B > divided by SIN of observed angle A-B. The radius is then used to plot > the circle center on the chart arcing an intersection off A and B. > From the circle center the full circle can be made which will have the > observer, mark A and B on the perimeter. Getting a fix requires > plotting a second circle between mark C and A or B. If variation and > deviation are known then a single bearing to A or B can be plotted to > intersect the circle to produce a fix. The intersection of two > horizontal angle circles is the better fix though. See David Fleming's > previous post for additional explanations and a description of the > standard method for plotting the horizontal angle circle. > > Greg Rudzinski > Ok, I had to rediscover Proposition III.20 from Euclid's Elements regarding the relationship between an arc inscribed on the circumference of a circle and the central angle. I'm convinced now.