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See searches and references containing RIGHT TRIANGLE!RIGHT TRIANGLE
Triangle containing a 90-degree angle
A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular
Right_triangle
Right triangle with a feature making calculations on the triangle easier
A special right triangle is a right triangle with some notable feature that makes calculations on the triangle easier, or for which simple formulas exist
Special_right_triangle
Shape with three sides
scalene triangle. Isosceles triangle Equilateral triangle Scalene triangle Regarding the angles, a triangle in which one of the angles is a right angle
Triangle
Property of geometry, also used to generalize the notion of "distance" in metric spaces
^{1}} , and the triangle inequality expresses a relationship between absolute values. In Euclidean geometry, for right triangles the triangle inequality is
Triangle_inequality
Integer side lengths of a right triangle
positive integer k. A triangle whose side lengths are a Pythagorean triple is a right triangle and called a Pythagorean triangle. A primitive Pythagorean
Pythagorean_triple
Triangles without a right angle
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
Acute_and_obtuse_triangles
Triangle with at least two sides congruent
the equilateral triangle as a special case. Examples of isosceles triangles include the isosceles right triangle, the golden triangle, and the faces of
Isosceles_triangle
Rational right triangles cannot have square area
Fermat's right triangle theorem is a non-existence proof in number theory, published in 1670 among the works of Pierre de Fermat, soon after his death
Fermat's right triangle theorem
Fermat's_right_triangle_theorem
Relation between sides of a right triangle
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
Pythagorean_theorem
90° angle (π/2 radians)
a right angle in a triangle is the defining factor for right triangles, making the right angle basic to trigonometry. The meaning of right in right angle
Right_angle
Perpendicular line segment from a triangle's side to opposite vertex
the triangle is acute. For a right triangle, the orthocenter coincides with the vertex at the right angle. For an equilateral triangle, all triangle centers
Altitude_(triangle)
Ancient Greek philosopher (c. 626 – c. 545 BC)
. he has proved himself mathematician." A right triangle with two equal legs is a 45-degree right triangle, all of which are similar. The length of the
Thales_of_Miletus
Generalization of Pythagorean theorem
the Pythagorean theorem, which holds only for right triangles: if γ {\displaystyle \gamma } is a right angle then cos γ = 0 {\displaystyle \cos
Law_of_cosines
leg of the right triangle to be the base of the triangle, the corresponding altitude of the triangle is the other leg. Any other triangle, choosing an
Area_of_a_triangle
Area of geometry, about angles and lengths
In particular, the trigonometric functions relate the angles of a right triangle with ratios of its side lengths. The field emerged in the Hellenistic
Trigonometry
Geometry of figures on the surface of a sphere
quadrantal triangle can be derived from those for a right-angled triangle. The polar triangle of a polar triangle is the original triangle. If the 3 ×
Spherical_trigonometry
Shape subdivided into copies of itself
equilateral triangle, it will also be a rep-tile. A right triangle is a triangle containing one right angle of 90°. Two particular forms of right triangle have
Rep-tile
Right triangle related to the golden ratio
A Kepler triangle is a special right triangle with edge lengths in geometric progression. The ratio of the progression is φ {\displaystyle {\sqrt {\varphi
Kepler_triangle
On triangles inscribed in a circle with a diameter as an edge
AD) statement that Thales "was the first to inscribe in a circle a right-angle triangle". Thales was claimed to have traveled to Egypt and Babylonia, where
Thales's_theorem
Functions of an angle
goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences
Trigonometric_functions
Intersection of triangle altitudes
the triangle is acute. For a right triangle, the orthocenter coincides with the vertex at the right angle. For an equilateral triangle, all triangle centers
Orthocenter
Polygonal curve made from right triangles
composed of right triangles, placed edge-to-edge. It was named after Theodorus of Cyrene. The spiral is started with an isosceles right triangle, with each
Spiral_of_Theodorus
Inverse functions of sin, cos, tan, etc.
{i}{z}}\right)&{}=\arcsin \left({\frac {1}{z}}\right)\end{aligned}}} Because all of the inverse trigonometric functions output an angle of a right triangle,
Inverse trigonometric functions
Inverse_trigonometric_functions
Two-dimensional packing problem
a right isosceles triangle is a packing problem where the objective is to pack n unit circles into the smallest possible isosceles right triangle. Minimum
Circle packing in an isosceles right triangle
Circle_packing_in_an_isosceles_right_triangle
Triangular array of the binomial coefficients
{Re}}\left({\text{Fourier}}\left[{\frac {\sin(x)^{5}}{x}}\right]\right)} compose the 4th row of the triangle, with alternating signs. This is a generalization
Pascal's_triangle
Fundamental trigonometric functions
The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the
Sine_and_cosine
Type of triangle
The solution is particularly simple for skinny triangles that are also isosceles or right triangles: in these cases the need for trigonometric functions
Skinny_triangle
Rectangle with side lengths in the golden ratio
adjoining right triangles, tracing a whirl of converging golden rectangles. The logarithmic spiral through the vertices of adjacent triangles has polar
Golden_rectangle
Theorem about right triangles
geometry, the right triangle altitude theorem or geometric mean theorem is a relation between the altitude on the hypotenuse in a right triangle and the two
Geometric_mean_theorem
of Bosnia and Herzegovina contains a medium blue field with a yellow right triangle separating said field, and there are seven full five-pointed white stars
Flag of Bosnia and Herzegovina
Flag_of_Bosnia_and_Herzegovina
Circle that passes through the vertices of a triangle
triangles, rectangles, isosceles trapezoids, right kites, and regular polygons are cyclic, but not every polygon is. The circumcircle of a triangle can
Circumcircle
Triangle formed by tangents to a given triangle's circumcircle at its vertices
tangential triangle of a reference triangle (other than a right triangle) is the triangle whose sides are on the tangent lines to the reference triangle's circumcircle
Tangential_triangle
Idea for signaling extraterrestrial beings from Earth
right triangle proposal is an idea attributed to Carl Friedrich Gauss for a method to signal extraterrestrial beings by constructing an immense right
Gauss's Pythagorean right triangle proposal
Gauss's_Pythagorean_right_triangle_proposal
geometry, triangle inequalities are inequalities involving the parameters of triangles, that hold for every triangle, or for every triangle meeting certain
List_of_triangle_inequalities
Hyperbolic analogues of trigonometric functions
The hyperbolic functions may be defined in terms of the legs of a right triangle covering this sector. In complex analysis, the hyperbolic functions
Hyperbolic_functions
Shape with three equal sides
triangle is a triangle with three sides of equal length and three equal angles. It is a regular polygon, occasionally known as the regular triangle.
Equilateral_triangle
Unit of length in astronomy
right triangle, the long leg of the triangle will measure the distance from the Sun to the star. A parsec can be defined as the length of the right triangle
Parsec
Longest side of a right-angled triangle, the side opposite of the right angle
of a right triangle that is opposite to the right angle. It is always the longest side of the triangle. The other two sides of a right triangle are called
Hypotenuse
Relation between the side lengths and altitude of a right triangle
endpoints of the hypotenuse of a right triangle △ABC. Let D be the foot of a perpendicular dropped from C, the vertex of the right angle, to the hypotenuse.
Inverse_Pythagorean_theorem
Circles tangent to all three sides of a triangle
incircle is a triangle center called the triangle's incenter. An excircle or escribed circle of the triangle is a circle lying outside the triangle, tangent
Incircle_and_excircles
Spacing between equally-spaced square numbers
Pythagorean triangle, a right triangle whose sides are integers. Congrua are also closely connected with congruent numbers, the areas of right triangles whose
Congruum
Relation between sine and cosine
definitions of the sine and cosine functions in terms of the sides of a right triangle are: sin θ = o p p o s i t e h y p o t e n u s e = b c cos θ = a
Pythagorean trigonometric identity
Pythagorean_trigonometric_identity
Geometric shape
semicircle and the third vertex elsewhere on the semicircle is a right triangle, with a right angle at the third vertex. All lines intersecting the semicircle
Semicircle
Polyhedron with four faces
length. It is not possible to construct a disphenoid with right triangle or obtuse triangle faces. An orthoscheme is an irregular simplex that is the
Tetrahedron
Impossible object
it. The tribar/triangle appears to be a solid object, made of three straight beams of square cross-section that meet pairwise at right angles at the vertices
Penrose_triangle
Prime number congruent to 1 mod 4
Pythagorean triangle. For instance, the number 5 is a Pythagorean prime; 5 {\displaystyle {\sqrt {5}}} is the hypotenuse of a right triangle with legs 1
Pythagorean_prime
Babylonian clay tablet of numbers in Pythagorean triples
s^{2}+l^{2}=d^{2}} , the rule that equates the sum of the squares of the legs of a right triangle to the square of the hypotenuse. The era in which Plimpton 322 was written
Plimpton_322
Concept in geometry
geometry to show that the area inside a circle is equal to that of a right triangle whose base has the length of the circle's circumference and whose height
Area_of_a_circle
Line constructed from a triangle
triangle that is not equilateral. It is a central line of the triangle, and it passes through several important points determined from the triangle,
Euler_line
Circle with radius of one
circle's circumference, then |x| and |y| are the lengths of the legs of a right triangle whose hypotenuse has length 1. Thus, by the Pythagorean theorem, x and
Unit_circle
Triangle whose side lengths and area are integers
Heronian triangle (or Heron triangle) is a triangle whose side lengths a, b, and c and area A are all positive integers. Heronian triangles are named
Heronian_triangle
Partial results found before the complete proof
the area of a right triangle with integer sides can never equal the square of an integer. This result is known as Fermat's right triangle theorem. As shown
Proof of Fermat's Last Theorem for specific exponents
Proof_of_Fermat's_Last_Theorem_for_specific_exponents
Heronian triangle Pythagorean triangle Isosceles heronian triangle Primitive Heronian triangle Right triangle 30-60-90 triangle Isosceles right triangle Kepler
List of two-dimensional geometric shapes
List_of_two-dimensional_geometric_shapes
Line segment joining a triangle's vertex to the midpoint of the opposite side
a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has exactly three
Median_(geometry)
Triangle in hyperbolic geometry
In hyperbolic geometry, a hyperbolic triangle is a triangle in the hyperbolic plane. It consists of three line segments called sides or edges and three
Hyperbolic_triangle
construction within a fundamental triangle, (p q r), defined by internal angles as π/p, π/q, and π/r. Special cases are right triangles (p q 2). Uniform solutions
Lists of uniform tilings on the sphere, plane, and hyperbolic plane
Lists_of_uniform_tilings_on_the_sphere,_plane,_and_hyperbolic_plane
17th-century conjecture proved by Andrew Wiles in 1994
once. In ancient times it was known that a triangle whose sides were in the ratio 3:4:5 would have a right angle as one of its angles. This was used in
Fermat's_Last_Theorem
thereof, analogous to the Pythagorean theorem characterizing right triangles as the triangles satisfying the formula a 2 + b 2 = c 2 {\displaystyle a^{2}+b^{2}=c^{2}}
Automedian_triangle
Geometric construction
sides of a right triangle, whose outer boundaries are semicircles and whose inner boundaries are formed by the circumcircle of the triangle, then the areas
Lune_of_Hippocrates
Hypotenuse of right triangle from its sides
on the real numbers that computes the length of the hypotenuse of a right triangle, given its two sides. Like the more familiar addition and multiplication
Pythagorean_addition
Symmetric subdivision in hyperbolic geometry
face-transitive) or semi-regular (if neither edge- nor face-transitive). For right triangles (p q 2), there are two regular tilings, represented by Schläfli symbol
Uniform tilings in hyperbolic plane
Uniform_tilings_in_hyperbolic_plane
Square whose vertices lie on a triangle
that both apply to triangles. Every acute triangle has three inscribed squares, one lying on each of its three sides. In a right triangle there are two inscribed
Inscribed square in a triangle
Inscribed_square_in_a_triangle
'mathematical right angle bracket' is not the same character as U+003E 'greater than', U+203A 'single right-pointing angle quotation mark', or U+3009 'right angle
List of XML and HTML character entity references
List_of_XML_and_HTML_character_entity_references
Shape with four equal sides and angles
lies on a side of the triangle. Every acute triangle has three inscribed squares, one for each of its three sides. A right triangle has two inscribed squares
Square
1911 factory fire in New York City
The Triangle Shirtwaist Factory fire occurred in the Greenwich Village neighborhood of Manhattan, a borough of New York City, on Saturday, March 25, 1911
Triangle Shirtwaist Factory fire
Triangle_Shirtwaist_Factory_fire
Object used in engineering and technical drawing
square or triangle (American English) is an object used in engineering and technical drawing, with the aim of providing a straightedge at a right angle or
Set_square
sided Triangle Acute triangle Equilateral triangle Isosceles triangle Obtuse triangle Rational triangle Right triangle 30-60-90 triangle Isosceles right triangle
List_of_mathematical_shapes
Mathematical model of the physical space
any triangle, two angles taken together in any manner are less than two right angles." (Book I proposition 17) and the Pythagorean theorem "In right-angled
Euclidean_geometry
Side of a right triangle
In a right triangle, a cathetus (originally from Greek κάθετος, "perpendicular"; plural: catheti), commonly known as a leg, is either of the sides that
Cathetus
Triangle with integer side lengths
An integer triangle or integral triangle is a triangle all of whose side lengths are integers. A rational triangle is one whose side lengths are rational
Integer_triangle
On sets of points with integer distances
multiples of one of the acute angles of an integer-sided right triangle (such as the triangle with side lengths 3, 4, and 5) has this property. This construction
Erdős–Anning_theorem
Diagram in Austrian economics
Austrian business cycle theory. The diagram is most commonly drawn as a right triangle, although later authors have used trapezoids and other variants. In
Hayekian_triangle
Property of all triangles on a Euclidean plane
ABD=90^{\circ }} , by Thales's theorem. Since △ A B D {\displaystyle \triangle ABD} is a right triangle, sin δ = opposite hypotenuse = c 2 R , {\displaystyle \sin
Law_of_sines
Interference pattern
diagonal. The long diagonal 2D is the hypotenuse of a right triangle and the sides of the right angle are d(1 + cos α) and p. The Pythagorean theorem
Moiré_pattern
Trigonometric values in terms of square roots and fractions
isosceles right triangle with leg length 1. Since two of the angles in an isosceles triangle are equal, if the remaining angle is 90° for a right triangle, then
Exact_trigonometric_values
Spherical triangle that can be used to tile a sphere
of the half-circle. "2" means a right triangle. When these are whole numbers, the triangle is called a Möbius triangle, and corresponds to a non-overlapping
Schwarz_triangle
Number, approximately 1.618
circle are in golden proportion. The Kepler triangle, named after Johannes Kepler, is the unique right triangle with sides in geometric progression: 1 :
Golden_ratio
Natural number
well as the length of the hypotenuse of the smallest integer-sided right triangle, making part of the smallest Pythagorean triple (3, 4, 5). 5 is the
5
Natural number
deficient number. 777 is a congruent number, as it is possible to make a right triangle with rationally numbered side lengths whose area is 777. According to
777_(number)
Non-sinusoidal waveform
Triangle wave sound sample 5 seconds of triangle wave at 220 Hz Problems playing this file? See media help. Additive Triangle wave sound sample After
Triangle_wave
American business news channel
introduced in the 2023 rebranding (including its neon blue corporate color, right triangle icons, and its associated on-air graphics—which were maintained with
CNBC
Prism with a 3-sided base
edges pair with each triangle's vertex and if they are perpendicular to the base, the triangular prism is a right prism. A right triangular prism may
Triangular_prism
Branch of pure mathematics
modular arithmetic, and Fermat's Last Theorem, as well as proved Fermat's right triangle theorem. He also studied prime numbers, the four-square theorem, and
Number_theory
Solid with eight equal triangular faces
geometry, a regular octahedron is an eight-sided polyhedron with equilateral triangles as its faces. Known for its highly symmetrical form, the regular octahedron
Regular_octahedron
Shape with five sides
the two right triangles DCM and QCM are depicted below the circle. Using Pythagoras' theorem and two sides, the hypotenuse of the larger triangle is found
Pentagon
Simplex formed from a right-angled path
is a type of simplex. The orthoscheme is the generalization of the right triangle to simplex figures of any number of dimensions. Orthoschemes are defined
Schläfli_orthoscheme
Collection of proofs of equations involving trigonometric functions
oldest and most elementary definitions are based on the geometry of right triangles and the ratio between their sides. The proofs given in this article
Proofs of trigonometric identities
Proofs_of_trigonometric_identities
North American collegiate fraternity
a triangle is mentioned in this article, a 3-4-5 right triangle of the first quadrant is what is meant. The present Acacia badge is a right triangle of
Acacia_Fraternity
Size of a two-dimensional surface
parallelogram can be subdivided into a trapezoid and a right triangle, as shown in figure to the left. If the triangle is moved to the other side of the trapezoid
Area
Mathematics used in ancient Mesopotamia
first suggested half a century ago, and the second by some sort of right-triangle problems. Babylonians knew the common rules for measuring volumes and
Babylonian_mathematics
Natural number between 89 and 91
90 degrees is called a right angle. In normal space, the interior angles of a rectangle measure 90 degrees each, while in a right triangle, the angle opposing
90_(number)
Topics referred to by the same term
another given side Adjacent side (right triangle), the side (or cathetus) of a right triangle that touches a given non-right angle Adjacent flag (geometry)
Adjacent
Conflagration mapping platform developed by NASA
user defined sequence of connected line segments, here the isosceles right triangle of the Virgo interferometer with sides 3 km + 3 km + 3 √2 km ≈ 10.24 km
Fire Information for Resource Management System
Fire_Information_for_Resource_Management_System
Conformal map projection
Peirce in 1877. Each octant projects onto an isosceles right triangle, with eight such triangles arranged into a square. The name quincuncial refers to
Peirce_quincuncial_projection
Place in Texas, United States
Angel's Triangle (formerly Devil's Triangle) is a neighborhood located in Northeast El Paso in El Paso, Texas. It lies within a right triangle bordered
Angel's Triangle, El Paso, Texas
Angel's_Triangle,_El_Paso,_Texas
Number, approximately 2.41421
adjoining right triangles, tracing a whirl of converging silver rectangles. The logarithmic spiral through the vertices of adjacent triangles has polar
Silver_ratio
Index of articles associated with the same name
theorem, about expressing integers as a sum of polygonal numbers Fermat's right triangle theorem, about squares not being expressible as the difference of two
Fermat's_theorem
Length of a line segment
} This can be seen by applying the Pythagorean theorem to a right triangle with horizontal and vertical sides, having the line segment from p {\displaystyle
Euclidean_distance
Plane fractal constructed from squares
mathematician Pythagoras because each triple of touching squares encloses a right triangle, in a configuration traditionally used to depict the Pythagorean theorem
Pythagoras_tree_(fractal)
Illustration of the Pythagorean theorem
right triangle with the three squares has reminded various writers of an insect, so the 'insect' sense of the Greek word came to be applied to right triangles
Bride's_Chair
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RIGHT TRIANGLE