Integer triangle not) satisfy formula_151. We can generate the full equivalence class of similar triangles that satisfy B=3A by using the formulas where formula_28 and formula_27 are integers such that formula_157. Note that all triangles with B = 3A (whether with integer sides or not) satisfy formula_158. The only integer triangle with three rational angles (rational numbers of degrees, or equivalently rational fractions of a full turn) is the equilateral triangle. This is because integer sides imply three rational cosines by the law of cosines, and by Niven's theorem a rational cosine coincides with a rational angle if and only if the
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: