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

60 Solution of Spherical Triangles.
The formulae (263)-(265) may be replaced by the following:I tan (45~ s"') = I tan (s' + s") + tan (d' + d") - tan (45~ - d"').
(266)
I tan d' = I tan (s' - s") + I tan (d' - d") - 1 tan s"'. (267)
Or thus:-Let fall the perpendicular CD; then, denoting the
arc AD by 4 and the angle A CD by I, we have, from the
right-angled triangle A CD,
tan 4 = tan b cos A, tan ti = cot A/cos b.
C
D
Fig. 19.
Then the sought parts are given by the equations
sin B = sin b sin A/sin a, cos (c - )) = cos a cos 4/cos b,
cos (C - f) = cot a tan b cos i.
EXERCISES.-XVIII.
1. Given a= 73~ 39'38", b=120~ 55' 35", A = 88~ 52' 42";
find B, C, c.
2., a=150 57 5, b=134 15 54, A=144 22 42;
find B, C. c.
3., a= 20 16 38, b= 56 19 40, A= 20 9 54;
find B, C,.