Law of cosines . The power of the point with respect to the circle is equal to both and . Therefore, which is the law of cosines. Using algebraic measures for line segments (allowing negative numbers as lengths of segments) the case of obtuse angle () and acute angle () can be treated simultaneously. By using the law of sines and knowing that the angles of a triangle must sum to 180 degrees, we have the following system of equations (the three unknowns are the angles): Then, by using the third equation of the system, we obtain a system of two equations in
Euler angles reached as follows: In sum, the three elemental rotations occur about "z", "x" and "z". Indeed, this sequence is often denoted "z-x-z" (or 3-1-3). Sets of rotation axes associated with both proper Euler angles and Tait–Bryan angles are commonly named using this notation (see above for details). There are six possibilities of choosing the rotation axes for proper Euler angles. In all of them, the first and third rotation axes are the same. The six possible sequences are: Angles are commonly defined according to the right-hand rule. Namely, they have positive values when they represent a rotation that appears clockwise