WOLFRAM|DEMONSTRATIONS PROJECT

Spherical Right Triangles

point A

1.0472

point B

1.0472

show sphere

Draw a spherical triangle

ABC

on the surface of a unit sphere centered at

O=(0,0,0)

. Denote the arcs opposite the corresponding vertices as

a

,

b

,

c

. Let

α

,

β

,

γ

be the angles at the vertices

A

,

B

,

C

. Suppose

γ=π/2

, so that these become spherical right triangles. The following relations are then valid:

sina=sincsinα

sinb=sincsinβ

tana=sinbtanα

tanb=sinatanβ

cosc=cosacosb

cosα=cosasinβ

cosβ=cosbsinα

sina=sincsinαsina=sincsinαsina=sincsinα