Coastal Skipper and Yachtmaster Quiz · Position fixing

Only one lighthouse is in sight, so the navigator takes two bearings of it half an hour apart and plots this running fix. Where is the yacht at 1030?

A chart with a lighthouse on the coast at the top. Two pencil bearing lines run from the lighthouse down into the water: one to the lower left labelled 1000 bearing, one to the lower right labelled 1030 bearing. A line with two arrowheads, labelled run, starts on the 1000 bearing and ends at point B. Through B a third line is drawn parallel to the 1000 bearing, with double arrowheads at each end. Three points on the 1030 bearing are labelled A, B and C. The run line ends at B, the third line crosses the 1030 bearing at A, and the run line crosses the 1030 bearing at C.
A chart with a lighthouse on the coast at the top. Two pencil bearing lines run from the lighthouse down into the water: one to the lower left labelled 1000 bearing, one to the lower right labelled 1030 bearing. A line with two arrowheads, labelled run, starts on the 1000 bearing and ends at point B. Through B a third line is drawn parallel to the 1000 bearing, with double arrowheads at each end. Three points on the 1030 bearing are labelled A, B and C. The run line ends at B, the third line crosses the 1030 bearing at A, and the run line crosses the 1030 bearing at C.
Show the answer

A: where the transferred position line crosses the 1030 bearing. In a running fix the first bearing is moved along by the run made good between the two bearings (course steered and distance logged, with leeway and tide allowed for). The yacht is where that transferred line crosses the second bearing. The run can be laid off from any point on the first line, so its end, B, is not itself the position.

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