Solid Angle Trigonometry? So I am interested in finding out how solid angle trigonometry works. Specifically, in 3 dimensional space, if we have three vectors reaching out from the origin, when we link the tips of the vectors together, we should get a tetrahedron. The idea is that since a tetrahedron is in some sense the three dimensional analog of a triangle, is there some way which we can use a 3D analog of trigonometry in this situation? Perhaps we could define the ratios of the areas of the sides of the tetrahedra, or functions as the lengths as functions of the solid angle between the three vectors? 
Upon googling, I haven't gotten much insight (all I got was things like the definition of solid angle). Perhaps this is due to there being a proper term for this concept which I am unaware of? If someone can enlighten me to the proper name of the concept, or better yet, if someone could provide me with links to important literature on the subject, it would be greatly appreciated. Thanks!

Interestingly, you added the spherical-trigonometry tag, which is precisely what you are after.
The generalization of planar trigonometry, which places the angles on the unit circle, places solid angles on the unit sphere. Much like a planar angle is measured by the arc length along the circle, a solid angle is measured by an area over the sphere.
The core of spherical trigonometry is devoted to the resolution of spherical triangles (delimited by three planes meeting at the origin and a portion of the sphere). The sides of such triangles are also (planar) angles.
Refer to the Wikipedia entry on spherical trigonometry https://en.wikipedia.org/wiki/Spherical_trigonometry.

