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

34 Connecting Sides and Angles of a Spherical Triangle.
FBE FE ED
Now OE = D OE; that is, sina = ssinAin c. (108')
FD FD BED
' OD EDB ' OD'?,, tanb cosA.tanc. (109')
EF EF F-)
" -O F^ = D ' OF; tan a= tanA. sinb. (110')
OD OD OF
OE = OF OE', cos c = cosa cosb. (113/)
O.E - OI OFE' OE
B
A
Fig. 15.
Multiply together (110') and the formula obtained by interchanging letters, and we get
-os aos= tan A tan B.
cos a cos b
Hence cos c = cot A cot B. (112')
Lastly, multiply crosswise (108') and the formula got from
(108') by interchange of letters; then
sin a cos B tan c = tan a sin A sin c;
sin 4 cos c
therefore cosB = incos = sin cosb. (111 )
cos a
37. The equations (108)-(111) are easily remembered by
comparing them with the corresponding equations for the
right-angled plane triangle. Thus