Figure 25A shows a spherical triangle ZSP. In all there are six quantities in a spherical triangle, namely, three angles Z, S and P and three sides z, s and p. If any three quantities are known, the remaining three can be computed from different formulae of the spherical trignometry given below.
Figure 25A
1. Sine formula
--------------- Eq 25A.1
2. Cosine formula
(i) cos Z = sin S sin P - cos S cos P --------------- Eq 25A.2
(ii) cos z = cos s cos p + sin s sin p cos Z --------------- Eq 25A.3
or
--------------- Eq 25A.3a
(iii) cos z cos s = sin z cot P - sin S sin P cos z --------------- Eq 25A.4
3. Half the angles formula
(i )
--------------- Eq 25A.5
(ii )
--------------- Eq 25A.6
(iii)
--------------- Eq 25A.7
Where 
Equation 25A.5 to 25A.7 should be used when there is some confusion about the signs of the angles. Because the value of the angle A / 2 is always less than 90°, there is no ambiguity. As far as possible, Eq. 25A.5 should be used when A < 90°. Eq. 25A.7 can be used for any value of the angle.
4. Half the sides Formula
(i)
--------------- Eq 25A.8
(ii )
--------------- Eq 25A.9
(iii )
--------------- Eq 25A.10
where 
5. Tangent of angles formulae
(i) 
--------------- Eq 25A.11a
(ii)
--------------- Eq 25A.11b
6. Tangent of sides formula
(i) 
--------------- Eq 25A.12a
(ii)
--------------- Eq 25A.12b
7. Combined formula
(i) sin z cos s = cos s sin p - sin s cos p cos Z --------------- Eq 25A.13
(ii) sin z sin s = sin s sin z --------------- Eq 25A.14