Your vessel is on course 312°pgc and you...

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Question 1 of 2066636ee928f7522a1c51a5bf

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?

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🔍 Key Concepts

• Relative bearing and abeam position (90° on the beam) • Converting between gyro compass course (pgc), gyro true, and true using gyro error • Using basic right-triangle / small-angle geometry to pass a fixed object at a given closest point of approach (CPA)

💭 Think About

• If the lighthouse is dead ahead now, what true bearing is it on, once you correct for the gyro error? • To have the lighthouse 1.5 miles abeam to starboard when you are 10 miles from it now, what small change in track (in degrees) would roughly give that lateral offset? • After you find the desired true course, how do you convert that back to a pgc course using a 3°E gyro error?

✅ Before You Answer

• Be clear on the sign: with 3°E gyro error, is gyro reading higher or lower than true? (Remember "east, least" for true = gyro – E). • Confirm whether the final answer needs to be in true or pgc by reading each choice carefully. • Check that your geometry makes sense: a 1.5‑mile offset over 10 miles should correspond to a small angle, not a very large alteration.

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