🔍 Key Concepts
• Use the great circle (orthodromic) sailing formulas: one for distance using the difference in longitude and both latitudes, and one for initial course at departure.
• Work entirely in degrees and minutes converted to decimal degrees or radians consistently before using trig functions.
• Remember that in the North Atlantic, going from western longitude to small eastern longitude, the longitude difference (Δλ) must be handled carefully for sign and size.
💭 Think About
• First, compute the difference in latitude and the difference in longitude between the two positions. Is Δλ reasonably large for an ocean crossing from the western Atlantic to near the English Channel?
• Next, use the great circle distance formula to find the central angle (in degrees or radians). Does the distance you compute fall in the 3100–3300 NM range? Which option is closest?
• Then determine the initial great circle course at the point of departure. From a position off the U.S. East Coast heading toward the approaches to Europe, should your initial true course be generally northeast (between about 040° and 060°), southeast, or northwest? Which options match that general direction?
✅ Before You Answer
• Verify you have converted minutes to decimal degrees correctly (e.g., 51.0' = 0.85°).
• Check that you are using nautical miles, where 1 minute of arc on a great circle equals 1 NM, and distance = central angle (in minutes of arc).
• Confirm the quadrant of the initial course: from 27°N, 71°W to 49°N, 6°W, should the course be in the northeast (between 000° and 090°) or some other quadrant? Eliminate any options that contradict this reasoning.