Oblique Spherical Triangle

Definition of oblique spherical triangle
Spherical triangles are said to be oblique if none of its included angle is 90° or two or three of its included angles are 90°. Spherical triangle with only one included angle equal to 90° is a right triangle.
 

Sine law
sinasinA=sinbsinB=sincsinC
 

000-oblique-spherical-triangle.gif

 

Cosine law for sides
cosa=cosb cosc+sinb sinc cosA

cosb=cosa cosc+sina sinc cosB

cosc=cosa cosb+sina sinb cosC
 

Cosine law for angles
cosA=cosB cosC+sinB sinC cosa

cosB=cosA cosC+sinA sinC cosb

cosC=cosA cosB+sinA sinB cosc
 

Napier's analogies
sin12(AB)sin12(A+B)=tan12(ab)tan12C

cos12(AB)cos12(A+B)=tan12(a+b)tan12C

sin12(ab)sin12(a+b)=tan12(AB)cot12c

cos12(ab)cos12(a+b)=tan12(A+B)cot12c