🔍 Key Concepts

• Great circle sailing formulas for distance and course on a sphere • Relationship between difference of longitude (DLo) and the sine/cosine of the latitudes in great circle problems • How initial course near the departure latitude compares to a simple rhumb-line (Mercator) bearing for a rough reasonableness check

💭 Think About

• First, compute (or estimate) the difference of longitude between the two positions and decide whether you are mainly crossing east–west or north–south. • Use the standard great circle distance formula involving the cosine of the central angle; think about which answer ranges are reasonable for a North Atlantic crossing at these latitudes. • Compare the direction of travel on the globe: from 9°W to 81°W and from 38°N to 32°N—should the initial true course be generally westward or eastward, and slightly toward higher or lower latitude?

✅ Before You Answer

• Be sure you are using west longitude correctly when finding DLo (watch the signs). • Check that your computed central angle (in degrees) makes sense before converting it to miles using 60 NM per degree. • Verify that the initial true course you obtain agrees with the general sense of the track: are you steering generally southwest, northwest, southeast, or northeast from the departure point?