suppose that we observe target c from two points a and b a distance a part and we wish to compute the range r=AC from the known bearings θ1=∠ABC and θ2=∠CAZ where Z lies on the line AB produced. We suppose that r is something like 5000 meters while AB is more like 50 meters or less. We need some restriction on θ1 so we assume π/4≤θ1≤π/2. Let X be the point on CB so that CX=r. Show that ∠ACX=θ2−θ1 and that AX=2r sin [(θ2−θ1)/2].