Determining Latitude Of Vertex

The great circle distance from Lat. 35° 08' S, Long. 019° 26' E to Lat. 33° 16' S; Long. 115° 36' E is 4559 nautical miles and the initial course is 121° T. Determine the latitude of the vertex.

Given:

             Lat1 = 35° 08' S
             Lat2 = 33° 16' S
          Long1 = 019° 26' E
          Long2 = 115° 36' E
Initial Course = 121° T

What is asked?

Latitude of vertex

Solution:

This is the formula to getting the latitude of vertex...

Cos Lat Vertex = Cos Lat1 × Sin I.C.

Cos Lat Vertex = Cos 35° 08' × Sin 121°
Cos Lat Vertex = 0.70100
       Lat Vertex = Inv Cos 0.70100
       Lat Vertex = 45° 30' S

Note:
         Name the Latitude vertex according to the name of Lat1.                        

Latitude Of Vertex

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