🔍 Key Concepts

• Relative bearing vs. true/pgc course and how to convert relative bearings to true directions from the ship’s head • Right triangle / off-track distance problems: relating closest point of approach (CPA) abeam distance, present distance, and change of course • Using small-angle geometry or law of cosines/sines to find the course that gives a specified abeam distance from a fixed object

💭 Think About

• First sketch the situation: your current course line, the light’s relative position (13° on the port bow), and where you want your track to be when you pass 4 miles abeam of the light to port. • Convert the 13° port-bow bearing into a true/pgc bearing of the light from your vessel. How does that line of position relate to the desired parallel track that passes 4 miles abeam? • Think about whether you need to turn toward or away from the light to increase the eventual minimum distance from 12.3 miles downrange to 4 miles abeam, and by roughly how many degrees that turn is likely to be.

✅ Before You Answer

• Be clear which angles are relative bearings (from the ship’s head) versus compass courses (pgc). Don’t mix them. • Verify that your geometry uses the current distance to the light (12.3 miles) and the desired abeam distance (4 miles) correctly in the triangle you set up. • Before picking an answer, check whether your chosen course would put the light on the correct side (to port) at the time you are abeam, not starboard.