Hyperbolic Triangle - Euclidean Geometry

Euclidean Geometry

In the foundations of the hyperbolic functions sinh, cosh and tanh, a hyperbolic triangle is a right triangle in the first quadrant of the Cartesian plane

with one vertex at the origin, base on the diagonal ray y = x, and third vertex on the hyperbola

The length of the base of such a triangle is

and the altitude is

where u is the appropriate hyperbolic angle.

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