Right triangle a right triangle. For a given angle, a right triangle may be constructed with this angle, and the sides labeled opposite, adjacent and hypotenuse with reference to this angle according to the definitions above. These ratios of the sides do not depend on the particular right triangle chosen, but only on the given angle, since all triangles constructed this way are similar. If, for a given angle α, the opposite side, adjacent side and hypotenuse are labeled "O", "A" and "H" respectively, then the trigonometric functions are For the expression of hyperbolic functions as ratio of the sides of a
Kepler triangle if and only if that triangle is a Kepler triangle. A Kepler triangle can be constructed with only straightedge and compass by first creating a golden rectangle: Kepler constructed it differently. In a letter to his former professor Michael Mästlin, he wrote, "If on a line which is divided in extreme and mean ratio one constructs a right angled triangle, such that the right angle is on the perpendicular put at the section point, then the smaller leg will equal the larger segment of the divided line." In the Kepler triangle with sides formula_8 consider: Then the perimeters of the