Your vessel is on course 312°pgc and you sight a lighthouse dead ahead at a range of 10 miles. The gyro error is 3°E. What course would you steer to leave the lighthouse 1.5 miles abeam to starboard?

Correct Answer: Option A — 304°pgc

The light is dead ahead, so the current distance off is 0. To pass 1.5 miles abeam, the required course change is arcsin(1.5 / 10) = 8.6 degrees. Subtracting this from the 312-degree pgc heading yields 303.4 degrees, which rounds to 304 degrees pgc to maintain the intended track.