A treatise on spherical trigonometry, and its application to geodesy and astronomy, with numerous examples. By John Casey.

74 Various Applications.
DEM.- cos MB + cos MC = 2 cos - cos M2'.
cos MA'. sin AG + cos MA. sin GA' = cos MG. sin AA';
cos MB+-cos =2cos-ca M' c os MG. sin GA
2 ( sin AG sin AG
M
A
G
B C
Fig. 26.
cos MA + cos MB + cos MC a sin AA'
2 cos -.
cos MG= 2 c sin AG'
a sin AG
since 2 cos -
2 sin GA'
cos MA + cos MB + cos MC sin AA' n
Hence = - = -
cos MilG sin GA' n'
17. Calculate the norm of the sides of BGC.
We have
n' sin GA' a sin (AA' - GA') a
n =sin.AA, 2 cos 2 sin GA' cos b + cos c = 2 cos. cos AA.
n sinAA" 2 sin GA' 2
We shall eliminate GA' and AA' between these equations. The second
gives
2 cos - sin GA' = sin AA' cos GA - cos AA' sin GA';
sin GA'2 cos 2 + cos A') = cos GA. sin AA';
* - 2 cos a + cos AA' = cos GA' = 1 - sin2AA',
n'2 1 1
4 cos2 + 4 cos - cos AA' + 1 4 cos2 + 2 (cos b + cos )+ 1
2 2 2