A vessel at LAT 38°36'N, LONG 11°36'W, heads for a destination at LAT 24°16'N, LONG 71°52'W. Determine the true course and distance by Mercator sailing.
• Mercator sailing relationship between difference of latitude, difference of longitude, and meridional parts • How to compute DMP (Difference of Meridional Parts) for the two latitudes (using a table or calculator) • How to find course from the right triangle formed by DMP (meridional difference) and departure (east‑west component)
• First, decide whether the general track is trending more east‑west or more north‑south by comparing the starting and destination latitudes and longitudes. What does that tell you about the approximate quadrant of the course (e.g., SW, SE, etc.)? • Compute the difference in latitude (in minutes) and the difference in longitude (in minutes). Which of those is larger, and how will that affect whether the course angle is closer to 0°, 90°, 180°, or 270°? • Think about what happens to distance in Mercator sailing: is it simply the difference in latitude, or is it related to the hypotenuse of a right triangle formed from the meridional difference and departure?
• Confirm the signs of ΔLat and ΔLong (N/S and E/W) to identify the correct course quadrant before looking at exact angles. • Ensure you use meridional parts (not just plain latitude in degrees) when forming the right triangle for Mercator sailing; the north‑south leg is the DMP, not raw ΔLat. • After finding the angle from your triangle, convert that to a true course in 0–360° notation and check that the distance you compute is in nautical miles, consistent with the units in the answer choices.
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