In other words, the quantity in the paragraph above is supposed to be equal to 1. Trigonometric formulas for hyperbolic triangles depend on the hyperbolic functions sinh, cosh, and tanh. Trigonometry of right triangles If C is a right angle then: The sine of angle A is the hyperbolic sine of the side opposite the angle divided by the hyperbolic sine of the hypotenuse. The cosine of angle A is the hyperbolic tangent of the adjacent leg divided by the hyperbolic tangent of the hypotenuse. The tangent of angle A is the hyperbolic tangent of the opposite leg divided by the hyperbolic sine of the adjacent leg. . The hyperbolic cosine of the adjacent leg to angle A is the cosine of angle B divided by the sine of angle A. . The hyperbolic cosine of the hypotenuse is the product of the hyperbolic cosines of the legs. . The hyperbolic cosine of the hypotenuse is also the product of the cosines of the angles divided by the product of their sines. Relations between angles We also have the following equations: Area The area of a right angled triangle is: The area for any other triangle is: also Angle of parallelism The instance of an omega triangle with a right angle provides the configuration to examine the angle of parallelism in the triangle. In this case angle B = 0, a = c = and , resulting in . Equilateral triangle The trigonometry formulas of right triangles also give the relations between the sides s and the angles A of an equilateral triangle (a triangle where all sides have the same length and all angles are equal). The relations are: General trigonometry Whether C is a right angle or not, the following relationships hold: The hyperbolic law of cosines is as follows: Its dual theorem is There is also a law of sines: and a four-parts formula: which is derived in the same way as the analogue formula in spherical trigonometry. See also Pair of pants (mathematics) Triangle group For hyperbolic trigonometry: Hyperbolic law of cosines Hyperbolic law of sines Lambert quadrilateral Saccheri quadrilateral References Further reading Svetlana Katok (1992) Fuchsian Groups, University of Chicago Press Triangle Types of triangles