You depart LAT 37° 36' N, LONG 123° 00' W,...

🔍 Key Concepts

• Mercator sailing relationship between difference in longitude, difference in latitude, and course:

\tan C = \frac{\Delta \text{Long (in minutes)}}{\Delta \text{Meridional Parts}}

or its equivalent form. • How to find difference in latitude from distance and course:

DLat = D \times \cos(C) / 60

and decide if you are going north or south. • Using the meridional parts (MP) table for the starting and ending latitudes to get

\Delta MP

, then using that to find

\Delta Long

💭 Think About

• Is your course 241° T taking you toward the equator or toward a pole? Use that to decide whether your latitude increases or decreases. • Once you compute the new latitude from the distance and course, what are the meridional parts for the initial and final latitudes, and what is their difference? • Given a southwesterly course, should your longitude increase or decrease in the western hemisphere, and by roughly how much for a 2000+ mile run?

✅ Before You Answer

• Make sure you convert the distance to difference in latitude in degrees using

DLat = D \times \cos(C) / 60

. • Verify you are using the angle from the meridian (0–90°) in the Mercator formula, not the full 0–360° course when applying

\tan C

. • After computing

\Delta Long

, check the sign and hemisphere: starting at 123° W and moving on a southwesterly course, should the final longitude be greater or less than 123° W?

You depart LAT 37° 36' N, LONG 123° 00' W, and steam 2022 miles on course 241° T. What is the longitude of your arrival by Mercator sailing?

LONG 154° 18.3' W

LONG 163° 18.2' W

LONG 163° 28.2' W

LONG 156° 51.7' W