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

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(A−B)sin12(A+B)=tan12(a−b)tan12C
cos12(A−B)cos12(A+B)=tan12(a+b)tan12C
sin12(a−b)sin12(a+b)=tan12(A−B)cot12c
cos12(a−b)cos12(a+b)=tan12(A+B)cot12c
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