Triangle of these conditions hold: (a) each of the angles is positive, and (b) the angles sum to 180°. If degenerate triangles are permitted, angles of 0° are permitted. Three positive angles "α", "β", and "γ", each of them less than 180°, are the angles of a triangle if and only if any one of the following conditions holds: the last equality applying only if none of the angles is 90° (so the tangent function's value is always finite). There are thousands of different constructions that find a special point associated with (and often inside) a triangle, satisfying some unique property:
Right triangle right triangle, see the hyperbolic triangle of a hyperbolic sector. The values of the trigonometric functions can be evaluated exactly for certain angles using right triangles with special angles. These include the "30-60-90 triangle" which can be used to evaluate the trigonometric functions for any multiple of π/6, and the "45-45-90 triangle" which can be used to evaluate the trigonometric functions for any multiple of π/4. Let "H", "G", and "A" be the harmonic mean, the geometric mean, and the arithmetic mean of two positive numbers "a" and "b" with "a" > "b". If a right triangle has legs "H"