🔍 Key Concepts

• Great circle sailing formulas for distance and initial course on a sphere • Converting degrees–minutes to decimal degrees before using trigonometric functions • Using the difference of longitude (DLo) correctly, including E/W signs

💭 Think About

• First, think about how to compute the central angle between two positions on the earth using their latitudes and difference of longitude. What trig relationship links those three values? • Once you know the central angle, how do you convert that angular distance in degrees to nautical miles on a great circle? • For the initial course, which trig ratio (sine, cosine, or tangent) would you use that involves the difference of longitude and the two latitudes?

✅ Before You Answer

• Make sure you convert all angles to the same format (either all decimal degrees or all radians) before putting them into formulas. • Check that your computed distance is in reasonable North Atlantic range between the Bahamas and the Bay of Biscay (rough order of 3,000–4,000 NM). • Verify that the initial course makes sense geographically: from about 25°N, 78°W toward 47°N, 6°W should be a northeasterly course (between roughly 040° and 060°T).