(Explanation is courtesy of player Bob C. of Chesteron, MD)

If the course is 25.25, and the first bearing is 25.93, then the angle between these bearings is .68 degrees. On a drawing, call this "A".

If the second bearing is 74.27, then the angle between this bearing and our course is 49.02 degrees. Because this angle is between the course line and the bearing line, you need to find the angle inside the triangle (between the bearing line and the leg we've already sailed). This angle equals 180 (the straight course line) minus 49.02, or 130.98 degrees. Call this angle "B".

Since the sum of the angles in a triangle equal 180 degrees, the final angle has to be 48.34 degrees. Call this angle "C".

The sides of the triangle created by the course line and bearing lines should be labeled with lower case letters a, b, and c, so that they are opposite the angles of their upper case counterparts. "a" is marked on a line opposite angle "A", etc.

We know side "c" is 18.75 nm as the distance we travelled.

The formula to solve for side "a", the distance from the second bearing to the lighthouse, is:

a = ("c" times the sin "A") divided by sin "C".

or

(18.75 times 0.01186) divided by 0.74710 = .2976 nautical miles

(Commander Bob used a NautiCalc Plus calculator for this problem, and arrived at a solution of .2978497 nm.)