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Similar to a Pythagorean triple, an Eisenstein triple (named after Gotthold Eisenstein) is a set of integers which are the lengths of the sides of a triangle where one of the angles is 60 or 120 degrees. The relation of such triangles to the Eisenstein integers is analogous to the relation of Pythagorean triples to the Gaussian integers.
An equilateral triangle may have integer sides with three rational angles as measured in degrees, [13] known for the only acute triangle that is similar to its orthic triangle (with vertices at the feet of the altitudes), [14] and the only triangle whose Steiner inellipse is a circle (specifically, the incircle).
Set square shaped as 45° - 45° - 90° triangle The side lengths of a 45° - 45° - 90° triangle 45° - 45° - 90° right triangle of hypotenuse length 1.. In plane geometry, dividing a square along its diagonal results in two isosceles right triangles, each with one right angle (90°, π / 2 radians) and two other congruent angles each measuring half of a right angle (45°, or ...
Every angle of an integer right triangle also has rational sine (see Pythagorean triple). If the angles of any triangle form an arithmetic progression then one of its angles must be 60°. [5] For integer triangles the remaining angles must also have rational cosines and a method of generating such triangles is given below.
The values of sine and cosine of 30 and 60 degrees are derived by analysis of the equilateral triangle. In an equilateral triangle, the 3 angles are equal and sum to 180°, therefore each corner angle is 60°. Bisecting one corner, the special right triangle with angles 30-60-90 is obtained.
The sum of the angles of a triangle is equal to a straight angle (180 degrees). [14] This causes an equilateral triangle to have three interior angles of 60 degrees. Also, it causes every triangle to have at least two acute angles and up to one obtuse or right angle.
An exterior angle of a triangle is an angle that is a linear pair (and hence supplementary) to an interior angle. The measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it; this is the exterior angle theorem. [34]
A right triangle ABC with its right angle at C, hypotenuse c, and legs a and b,. A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular, forming a right angle (1 ⁄ 4 turn or 90 degrees).