Example of great circle sailing calculation

Vessel depart from Richmond Lat 37°55’N Longitude 122°22’W to Malangas Lat 07°37’N Longitude 123°02’E.Find initial course,final course and distance make during voyage?

Lat  37°55’N                Long   122°22’W

Lat  07°37’N                Long   123°02’E

                                   -------------------------

                                  d’long A to B 114°36’ W  LHA=P

                                  d’long B to A 114°36’  E  LHA= 245°24’ P=114°36’

PA = 90° - 37°55’

      = 52°05’

PB = 90° - 07°37’

      = 82°23’

Dist AB

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cos AB = cos PA cos PB + sin PA sin PB cos APB

cos AB = cos 52°05’ cos 82°23’ + sin 52°05’ sin 82°23’ cos 114°36’

AB       = 104°07.57’

AB       = 6247.57 NM

Initial course

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cos A = cos PB - cos PA cos AB / (sin PA sin AB)

cos A = cos  82°23’ - cos 52°05’ cos 104°07.57’ / (sin 52°05’ sin 104°07.57’ )

A  =  N  68°19.71’W

A  =  291°40.29’ T

Final course

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cos B = cos PA - cos PB cos AB / (sin PB sin AB)

cos B = cos 52°05’ - cos 82°23’ cos 104°07.57’/ (sin  82°23’ sin 104°07.57’)

B  =   N  47°42.19’ E

Final  = S  47°42.19’ W

         = 227°42.19’ T