A lighthouse may serve to aid navigation in several ways. One way is illustrated in the following.
It is 1890 and a small freighter is cautiously following a NNE course along the coast at night. The shore is not visible in the darkness. The master of the freighter observes in the distance off the port bow the distinctive flashing light of a lighthouse. This is the only light he can see. When the light gradually gets closer the master will use this light to determine how far he is from the shore as he continues on this voyage along the coast.
At 10:15 P.M. when the light is now 4 points (45 degrees) off his port bow the master tells the helmsman to hold steady on NNE and to maintain headway at 10 knots. A few minutes later at 10:27 P.M. the master observes that the lighthouse is now abeam, directly beside his position. The master now determines that he is then 2 miles offshore from this lighthouse.
How did he determine this distance?