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

56 Solution of Spherical Triangles.
EXERCISES.-XVI.
1. Given a= 89~ 59' 59', b= 88~ 55' 58", c= 87~ 57' 57"; findA,B, C.
2.,, a=120 55 35, b=59 4 25, c=106 10 22;,,
3.,, a= 20 16 38, b=56 19 40, c= 66 20 44;,,
60. If only one angle, say A, be required, the formula for
tan A in terms of the sides is simpler than the foregoing.
Thus in logarithms,
I tan ~ A = ~ { sin (s - b) +1 sin (s - c) - I sins - l sin (s - a)}.
(254)
a = 82~ 33' 51" 1 sin (s - b) = 1*9788195
b =27 16 9 sin(s - c) = 12529286
c= 89 12 24 1-2317481
s =99 31 12 sins = 1-9939773
s-a=16 57 21 1 sin(s-a)= 1-4648388
- b = 72 15 3 1-4588161
s-c= 10 18 48 [.l7729320
l. tan I A = 1-8864660
Hence A = 75~ 11' 22".
61. Being given the three angles A, B, C, to calculate the sides.
From equations (181)-(185) we have
logL=: { tan E+ 1 tan (A-E)+ Itani(B-E)+ltan~( C-E)}.
(255)
l cot l s = log L - 1 tan E. (250')
I tan (s - a) = log L - l tan (.A - E). (251')
1 tan ~ (s - b) = log L - 1 tan } (B - E). (252')
1 tan i (s - c) = log L - 1 tan - (C - E). (253')
On comparing the equations (250')-(253') with (250)-(253)
of ~ 59, it will be seen that they are identical