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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
Euclid. Equilateral triangle Isosceles triangle Scalene triangle Right triangle Acute triangle Obtuse triangle All types of triangles are commonly found
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
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
Shape with three equal sides
An equilateral triangle is a triangle in which all three sides have the same length, and all three angles are equal. Because of these properties, the equilateral
Equilateral_triangle
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
'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
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
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
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
Special triangle in geometry
acute triangle The condition is 0 < x < 2 {\displaystyle 0<x<{\sqrt {2}}} . In this case x = 1 is valid for equilateral triangle. case 2) △ABC is right triangle
Calabi_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
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)
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
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
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
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
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
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
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
Number whose square is a given number
constructed, and once x {\displaystyle {\sqrt {x}}} has been constructed, the right triangle with legs 1 and x {\displaystyle {\sqrt {x}}} has a hypotenuse of x
Square_root
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
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
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
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
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
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
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
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)
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
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)
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
Optical illusion
13×5 right-angled triangle, but one has a 1×1 hole in it. The key to the puzzle is the fact that neither of the 13×5 "triangles" is truly a triangle, nor
Missing_square_puzzle
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)
Regular tiling of the plane
Scalene triangle p2 symmetry Scalene triangle pmg symmetry Isosceles triangle cmm symmetry Right triangle cmm symmetry Equilateral triangle p6m symmetry
Triangular_tiling
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
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
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
Physics problem related to laws of motion and gravity
3:4:5 are placed at rest at the vertices of a 3:4:5 right triangle, with the heaviest body at the right angle and the lightest at the smaller acute angle
Three-body_problem
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
Computer graphics 3D reference and test model
the Pythagorean theorem: construct a (2D) teapot on each side of a right triangle and the area of the teapot on the hypotenuse is equal to the sum of
Utah_teapot
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
Type of polarizer
together on their base (traditionally with Canada balsam) to form two right triangle prisms with perpendicular optic axes. Outgoing light beams diverge from
Wollaston_prism
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
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
1617 device for calculating products and quotients
square. Single-digit numbers are written in the bottom right triangle leaving the other triangle blank, while double-digit numbers are written with a digit
Napier's_bones
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
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
Dissection puzzle
right triangles (hypotenuse 1, sides √2/2, area 1/4) 1 medium right triangle (hypotenuse √2/2, sides 1/2, area 1/8) 2 small right triangles
Tangram
Ancient Chinese proof of the Pythagorean theorem
5 right triangle to demonstrate the Pythagorean theorem. However the Chinese people seem to have generalized its conclusion to all right triangles. The
Xuan_tu
RIGHT TRIANGLE
RIGHT TRIANGLE
Girl/Female
Indian
Bright light
Surname or Lastname
English
English : topographic name for someone who lived at the top of a hill or on a piece of raised ground, from Middle English heyt ‘summit’, ‘height’.
Boy/Male
Tamil
Light, Bright
Boy/Male
English
Bright light.
Boy/Male
Anglo, Australian, British, Christian, English
Craftsman; Carpenter
Boy/Male
English American Anglo Saxon
Craftsman.
Male
English
English occupational surname transferred to forename use, derived from Old English wryhta/wyrhta, WRIGHT means "craftsman."
Boy/Male
Tamil
Prakasha | பà¯à®°à®•ாஷÂ
Light, Bright
Prakasha | பà¯à®°à®•ாஷÂ
Girl/Female
Tamil
Bright light
Surname or Lastname
English
English : presumably a nickname for a strong man.
Surname or Lastname
English
English : from a Middle English nickname or personal name, meaning ‘bright’, ‘fair’, ‘pretty’, from Old English beorht ‘bright’, ‘shining’.English : from a short form of any of several Old English personal names of which beorht was the first element, such as Beorhthelm ‘bright helmet’. Compare Bert.Americanized form of German Brecht.Americanized spelling of German Breit.
Boy/Male
Tamil
Prajjwal | பà¯à®°à®œà¯à®œà¯à®µà®¾à®²
Bright light
Prajjwal | பà¯à®°à®œà¯à®œà¯à®µà®¾à®²
Surname or Lastname
English
English : nickname for a happy, cheerful person, from Middle English lyght, Old English lēoht ‘light’ (not dark), ‘bright’, ‘cheerful’.English : nickname for someone who was busy and active, from Middle English lyght, Old English līoht ‘light’ (not heavy), ‘nimble’, ‘quick’. The two words lēoht and līoht were originally distinct, but they were confused in English from an early period.English : nickname for a small person, from Middle English lite, Old English l̄t ‘little’, influenced by lyght as in 1 and 2.
Girl/Female
Tamil
Rossini | ரோஸஸீநீÂ
Light, Bright
Rossini | ரோஸஸீநீÂ
Boy/Male
English
Bright light.
Boy/Male
Tamil
Light, Bright
Boy/Male
English
Bright light.
Surname or Lastname
English, Scottish, and northern Irish
English, Scottish, and northern Irish : occupational name for a maker of machinery, mostly in wood, of any of a wide range of kinds, from Old English wyrhta, wryhta ‘craftsman’ (a derivative of wyrcan ‘to work or make’). The term is found in various combinations (for example, Cartwright and Wainwright), but when used in isolation it generally referred to a builder of windmills or watermills.Common New England Americanized form of French Le Droit, a nickname for an upright person, a man of probity, from Old French droit ‘right’, in which there has been confusion between the homophones right and wright.
Girl/Female
Muslim
Light, Bright
Girl/Female
Sikh
Light, Bright
RIGHT TRIANGLE
RIGHT TRIANGLE
Boy/Male
Tamil
God
Boy/Male
Indian
Name of a priest.
Boy/Male
Tamil
Joy, Happiness
Boy/Male
Indian, Kannada, Tamil
Debater; Orator; Well-versed in the Arts
Boy/Male
Hindu, Indian
Alias Name of Lord Shiva
Boy/Male
Indian
Gatherer, One who assembles
Boy/Male
Finnish, Hindu, Indian, Swedish
To Respond; Fortunate; Blessed; Happy
Girl/Female
Muslim
Beautiful, Bright, Brilliant, Shining
Girl/Female
Indian
Aurora, Morning light
Boy/Male
Muslim
Glory of kingdom, State
RIGHT TRIANGLE
RIGHT TRIANGLE
RIGHT TRIANGLE
RIGHT TRIANGLE
RIGHT TRIANGLE
a.
The right side; the side opposite to the left.
adv.
In a right or straight line; directly; hence; straightway; immediately; next; as, he stood right before me; it went right to the mark; he came right out; he followed right after the guide.
a.
Upright; erect from a base; having an upright axis; not oblique; as, right ascension; a right pyramid or cone.
a.
Containing a right angle or right angles; as, a right-angled triangle.
a.
That which is right or correct.
v. t.
To get sight of; to see; as, to sight land; to sight a wreck.
imp.
of Hight
adv.
In a right manner.
a.
To do justice to; to relieve from wrong; to restore rights to; to assert or regain the rights of; as, to right the oppressed; to right one's self; also, to vindicate.
a.
Situated or being on the right; nearer the right hand than the left; as, the right-hand side, room, or road.
imp. & p. p.
of Dight
superl
Having light; not dark or obscure; bright; clear; as, the apartment is light.
v. t.
To cause to fight; to manage or maneuver in a fight; as, to fight cocks; to fight one's ship.
a.
Straight; direct; not crooked; as, a right line.
a.
Fit; suitable; proper; correct; becoming; as, the right man in the right place; the right way from London to Oxford.
adv.
In a great degree; very; wholly; unqualifiedly; extremely; highly; as, right humble; right noble; right valiant.
adv.
According to the law or will of God; conforming to the standard of truth and justice; righteously; as, to live right; to judge right.
p. p.
of Hight
adv.
Rightly; correctly; in a right way or form; without mistake or crime; as, to worship God aright.
a.
Formed by right lines; rectilineal; as, a right-lined angle.