About: 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. 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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rdf:type	place yago:WikicatTriangles yago:Abstraction100002137 yago:Attribute100024264 yago:Figure113862780 yago:PlaneFigure113863186 yago:Polygon113866144 yago:Shape100027807 yago:Triangle113879320
rdfs:label	مثلثات قائمة خاصة (ar) Specialaj ortaj trianguloj (eo) Triángulo rectángulo especial (es) Special right triangle (en) Triângulo retângulo especial (pt) 特殊直角三角形 (zh)
rdfs:comment	في الهندسة الرياضية، نوعان من المثلثات القائمة: * «المثلثات القائمة على الزوايا» وتعتمد على النسبة بين زوايا المثلث القائم. * «المثلثات القائمة على الأضلاع» وتعتمد على النسبة بين أطوال أضلاع المثلث القائم. إن معرفة النسبة بين زوايا المثلث القائم تمكننا من معرفة أطوال أضلاعه. (ar) En geometrio, speciala orta triangulo estas orta triangulo kiu havas certajn angulojn aŭ rilatumojn inter longoj de lateroj. (eo) 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. (en) Um triângulo retângulo especial é um triângulo retângulo com alguma característica regular que facilita cálculos sobre um triângulo, ou para o qual existem fórmulas simples. Por exemplo, um triângulo retângulo pode ter ângulos formando relações características, como 45°–45°–90°. Este é denominado um triângulo retângulo "baseado em ângulo". Um triângulo retângulo "baseado em lado" tem lados com comprimentos formando relações de números inteiros, como 3 : 4 : 5, ou de outros números especiais, como a proporção áurea. Conhecendo as relações dos ângulos ou dos lados destes triângulos retângulos especiais é possível calcular rapidamente vários comprimentos em problemas geométricos sem a necessidade de recorrer a métodos mais avançados. (pt) 特殊直角三角形是一些有特殊性質的直角三角形，其特殊性質可能是使三角形的計算更加方便，或是存在一些較簡單的公式。例如有些三角形的內角有一些簡單的關係，例如45–45–90度三角形，這是各角有特殊關係的直角三角形。也有些直角三角形的各邊有特殊關係，例如各邊的比例可以用自然數表示，例如3 : 4 : 5，或是可以用黃金比例表示等。若在處理這些三角形時知道其特殊的邊關係或角關係，可以快速的計算一些幾何問題而不需用到一些較複雜的公式。 (zh) Un triángulo rectángulo especial es un tipo de triángulo rectángulo con alguna característica de regularidad que hace que los cálculos relativos al triángulo sean más fáciles, o para los cuales existen fórmulas simples. Por ejemplo, un triángulo rectángulo puede tener ángulos que forman relaciones simples, como 45° – 45° – 90°. Esto se llama un triángulo rectángulo basado en ángulos. Un triángulo rectángulo basado en lados es uno en el que las longitudes de los lados forman relaciones de números naturales, como por ejemplo 3 : 4 : 5, o de otros números especiales, como el número áureo. Conocer las relaciones de los ángulos o las proporciones de los lados de estos triángulos rectos especiales permite calcular rápidamente varias longitudes en problemas geométricos sin recurrir a métodos más (es)
foaf:depiction
dcterms:subject	Types of triangles Euclidean plane geometry
Wikipage page ID	2278116 (xsd:integer)
Wikipage revision ID	1090688968 (xsd:integer)
Link from a Wikipage to another Wikipage	Pythagorean triple Multiple (mathematics) Degree (angle) Hypotenuse Pell numbers Regular icosahedron Unit circle Decagon Geometric progression Niven's theorem Equilateral triangle Geometry Golden ratio Moritz Cantor Angle Berlin Papyrus 6619 De Iside et Osiride Pentagon Types of triangles Trigonometric functions Trigonometry Cosine (trigonometric function) Cotangent (trigonometric function) Spiral of Theodorus Altitude (triangle) Ancient Egypt Euclidean plane geometry Golden rectangle Gon (angle) Isosceles triangle Pythagorean theorem Reflection (mathematics) Hexagon Hyperbolic geometry Triangle group Area Arithmetic progression Heronian triangle Triangle Plutarch Square root of 2 Square root of 3 Square triangular number Tessellate Integer Integer triangle Middle Kingdom of Egypt Natural number Cathetus Radian Rational numbers Square Binary scaling Euclidean geometry Spherical geometry Right triangle Tangent (trigonometric function) Möbius triangle Pell equation Plane geometry Sine (trigonometric function)

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