Finding Arrival Longitude

You depart LAT 50° 06’ N, LONG 153° 06’ E and steam 879 miles on course 090°. What is the longitude of arrival?

Given:

           LAT 50° 06’ N

           LONG 153° 06’ E

           Distance = 879 miles

           Course = 090°

What is asked?

                        Longitude of arrival

Solution:

Step 1. Solving for the difference of longitude (Dlo). We can use the formula of parallel sailing in getting Dlo.

             Distance = Dlo × Cos Lat

                    

                     Dlo = Dist        

                               Cos Lat

                     Dlo = 879             

                               Cos 50° 06’

                     Dlo = 1370.33 miles (divide this by 60 to convert it into degrees)

                     Dlo = 1370.33 ÷ 60             

                     Dlo = 22° 50’ 20” E  (the sign is east because our ship is moving easterly, course  090°)

Step 2. Add Dlo to the longitude of departure (long₁) to get longitude of arrival (long₂).

                  

                  Long₁ =   153° 06’ E

                      Dlo = + 22° 50’ 20” E  (add because Long₁ and Dlo have the same name)

                  Long₂ =  175° 56’ 20” E  is the longitude of arrival