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Special right triangle information


Position of some special triangles in an Euler diagram of types of triangles, using the definition that isosceles triangles have at least two equal sides, i.e. equilateral triangles are isosceles.

A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. For example, a right triangle may have angles that form simple relationships, such as 45°–45°–90°. This is called an "angle-based" right triangle. A "side-based" right triangle is one in which the lengths of the sides form ratios of whole numbers, such as 3 : 4 : 5, or of other special numbers such as the golden ratio. Knowing the relationships of the angles or ratios of sides of these special right triangles allows one to quickly calculate various lengths in geometric problems without resorting to more advanced methods.

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Special right triangle

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A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist...

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Right triangle

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A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular...

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Triangle

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lengths of the legs and c is the length of the hypotenuse. Special right triangles are right triangles with additional properties that make calculations involving...

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Isosceles triangle

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the equilateral triangle as a special case. Examples of isosceles triangles include the isosceles right triangle, the golden triangle, and the faces of...

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Kepler triangle

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A Kepler triangle is a special right triangle with edge lengths in geometric progression. The ratio of the progression is φ {\displaystyle {\sqrt {\varphi...

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Triangle inequality

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^{1}} , and the triangle inequality expresses a relationship between absolute values. In Euclidean geometry, for right triangles the triangle inequality is...

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Acute and obtuse triangles

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acute triangle (or acute-angled triangle) is a triangle with three acute angles (less than 90°). An obtuse triangle (or obtuse-angled triangle) is a triangle...

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List of triangle topics

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theorem Sierpinski triangle (fractal geometry) Similarity (geometry) Similarity system of triangles Simson line Special right triangles Spieker center Spieker...

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Geometric mean theorem

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geometric mean theorem or right triangle altitude theorem is a relation between the altitude on the hypotenuse in a right triangle and the two line segments...

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Circumcircle

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circumcircle of a triangle is a circle that passes through all three vertices. The center of this circle is called the circumcenter of the triangle, and its radius...

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Penrose triangle

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it. The tribar/triangle appears to be a solid object, made of three straight beams of square cross-section which meet pairwise at right angles at the vertices...

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Nazi concentration camp badge

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black triangle with a Z notation (for Zigeuner, meaning Gypsy) to the right of the triangle's point. Roma were later assigned a brown triangle. Mentally...

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Sum of angles of a triangle

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the sum of angles of a triangle equals the straight angle (180 degrees, π radians, two right angles, or a half-turn). A triangle has three angles, one...

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Triangle center

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In geometry, a triangle center or triangle centre is a point in the triangle's plane that is in some sense in the middle of the triangle. For example,...

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Hypotenuse

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side of a right triangle opposite the right angle. It is the longest side of any such triangle; the two other shorter sides of such a triangle are called...

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Pythagorean theorem

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the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to...

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Hyperbolic triangle

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tangent circles. A triangle with one ideal vertex is called an omega triangle. Special Triangles with ideal vertices are: A triangle where one vertex is...

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Triangular prism

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the edges pair with each triangle's vertex and if they are perpendicular to the base, it is a right triangular prism. A right triangular prism may be both...

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Triangle Shirtwaist Factory fire

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The Triangle Shirtwaist Factory fire in the Greenwich Village neighborhood of Manhattan, New York City, on Saturday, March 25, 1911, was the deadliest...

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Exact trigonometric values

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the special right triangle with angles 30-60-90 is obtained. By symmetry, the bisected side is half of the side of the equilateral triangle, so one concludes...

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Pythagorean triple

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positive integer k. A triangle whose side lengths are a Pythagorean triple is a right triangle and called a Pythagorean triangle. A primitive Pythagorean...

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Trigonometry

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In particular, the trigonometric functions relate the angles of a right triangle with ratios of its side lengths. The field emerged in the Hellenistic...

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Reuleaux triangle

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A Reuleaux triangle [ʁœlo] is a curved triangle with constant width, the simplest and best known curve of constant width other than the circle. It is formed...

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