Trigonometry of a tetrahedron Clearly the sum of the angles of any side of the tetrahedron must be 180°. Since there are four such triangles, there are four such constraints on sums of angles, and the number of degrees of freedom is thereby reduced from 12 to 8. The four relations given by the sine law further reduce the number of degrees of freedom, from 8 down to not 4 but 5, since the fourth constraint is not independent of the first three. Thus the space of all shapes of tetrahedra is 5-dimensional. See: Law of sines The law of cosines for the tetrahedron
Olympic triangle be perfectly sharp, either, since it is a course. Traditionally the configuration of the triangle is an equilateral triangle (3 equal sides and 3 equal angles of 60 degrees) with a ratio of the windward leg to a reaching leg being 1:1. In that case the course length for the 9 legs described above is 9 times the length of the windward leg. The angle at each point of the triangle is 60 degrees. The windward leg is generally aligned with the average wind direction. Another configuration is a triangle with a right angle at the wing mark and 45