🔍 Key Concepts

• Great circle sailing formulas for distance and initial course on a spherical Earth • Converting latitudes and longitudes to radians and using the cosine formula for great-circle distance • Careful sign convention for North/South and East/West when plugging into formulas

💭 Think About

• What is the central angle between the two positions if you apply the great-circle cosine formula using their latitudes and the difference in longitude? • Once you know the central angle in degrees, how do you convert that to nautical miles on a great circle? • After getting the correct distance, how can you compute the initial great-circle course at departure, and which of the choices both matches the distance and is consistent with the general southwestward direction?

✅ Before You Answer

• Confirm that you converted south latitudes and west longitudes to the correct signs (N/S for latitude, E/W for longitude) before using trigonometric formulas • Double-check that you are using difference of longitude in the correct sense (taking E–E and getting the proper magnitude and direction) • Verify that your final distance in nautical miles reasonably matches the approximate rhumb-line distance (so the great-circle answer should be close but slightly shorter)