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 Task 1.  If a ship starts from position Latitude 30^o north, 15^o west and travels due east for 120 nautical miles, what will be its new position?

Solution:  

Lat.    =  30^o

Ddist   = 120 nautical miles.

Dlong  =  Ddist  x Sec Lat.

=  120 x Sec (30)

=  120 x 1.155

=  138.6’

=   2.3 ^o

Therefore, the ship’s new longitude is

15^o– 2.3^o  =  12.7^o W.

and so the new position is 30^o N.  12.7^o W.

Task 2.  If an aircraft flies from a position 50^oS. 60^oE to a position 50^o S. 80^oE. , how far has it flown?

Solution: 

Ddist   =  Dlong x Cos Lat.

=  20^o x 0.64

=  1200` x 0.64

=   768 nautical miles

Therefore, the aircraft has flown 768 nautical miles.

A thorough treatment of this topic can be found in the book Astro Navigation Demystified).