Trigonometry of a tetrahedron the role of "O" yields four such identities, but at most three of them are independent; if the "clockwise" sides of three of the four identities are multiplied and the product is inferred to be equal to the product of the "counterclockwise" sides of the same three identities, and then common factors are cancelled from both sides, the result is the fourth identity. Three angles are the angles of some triangle if and only if their sum is 180° (π radians). What condition on 12 angles is necessary and sufficient for them to be the 12 angles of some tetrahedron?
Solution of triangles third angle by using the angle sum property of a triangle, then find the other two sides using the law of sines. The general spherical triangle is fully determined by three of its six characteristics (3 sides and 3 angles). Note that the sides of a spherical triangle are measured by angular rather than linear units, based on the corresponding central angles. The solution of triangles for non-Euclidean spherical geometry has some differences from the planar case. For example, the sum of the three angles depends on the triangle. In addition, there are no unequal similar triangles, and so the