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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
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Anatomical area located in the right atrium of human heart
is located at the apex of the triangle. The base is formed by the coronary sinus orifice and the vestibule of the right atrium, and the hypotenuse is
Koch's_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
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
'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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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)
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
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
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)
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
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
Number that is not a ratio of integers
He did this by demonstrating that if the hypotenuse of an isosceles right triangle was indeed commensurable with a leg, then one of those lengths measured
Irrational_number
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
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
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
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
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
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
Straight figure with zero width and depth
also be proven geometrically by applying right triangle definitions of sine and cosine to the right triangle that has a point of the line and the origin
Line_(geometry)
Mathematical memory aids
trigonometric functions. The sine, cosine, and tangent ratios in a right triangle can be remembered by representing them as strings of letters, for instance
Mnemonics_in_trigonometry
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
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
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
Natural number
69 is a congruent number—a positive integer that is the area of a right triangle with three rational number sides—and an amenable number. 69 can be expressed
69_(number)
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
RIGHT TRIANGLE
RIGHT TRIANGLE
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
Boy/Male
English
Bright light.
Boy/Male
English
Bright light.
Girl/Female
Tamil
Bright light
Boy/Male
Anglo, Australian, British, Christian, English
Craftsman; Carpenter
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’.
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
English American Anglo Saxon
Craftsman.
Girl/Female
Muslim
Light, Bright
Girl/Female
Sikh
Light, Bright
Boy/Male
Tamil
Light, Bright
Boy/Male
Tamil
Prakasha | பà¯à®°à®•ாஷÂ
Light, Bright
Prakasha | பà¯à®°à®•ாஷÂ
Girl/Female
Indian
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.
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.
Surname or Lastname
English
English : presumably a nickname for a strong man.
Boy/Male
Tamil
Light, Bright
Girl/Female
Tamil
Rossini | ரோஸஸீநீÂ
Light, Bright
Rossini | ரோஸஸீநீÂ
Boy/Male
English
Bright light.
Male
English
English occupational surname transferred to forename use, derived from Old English wryhta/wyrhta, WRIGHT means "craftsman."
RIGHT TRIANGLE
RIGHT TRIANGLE
Girl/Female
Japanese
Older sister.
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : habitational name from places so named, of which there is one West Yorkshire and another in Suffolk, both probably deriving their name from an Old English personal name Heppa + worð ‘enclosure’. The surname is still found mainly in Yorkshire, so it seems that the first place is the more likely source of the surname.
Girl/Female
Hindu, Indian
Respectable Person; Goddess Saraswati
Boy/Male
Arabic, Muslim, Parsi
Glory of Religion (Islam)
Boy/Male
Hindu, Indian, Marathi
God of Kings
Girl/Female
British, English, Greek, Irish
Female Version of Darius; Rich; From Doris
Boy/Male
English
Friend.
Girl/Female
British, English
Boar; Friend
Girl/Female
Latin
Mother of Narcissus.
Female
English
Variant spelling of English Fanny, FANNI means "French."
RIGHT TRIANGLE
RIGHT TRIANGLE
RIGHT TRIANGLE
RIGHT TRIANGLE
RIGHT TRIANGLE
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.
Upright; erect from a base; having an upright axis; not oblique; as, right ascension; a right pyramid or cone.
adv.
Rightly; correctly; in a right way or form; without mistake or crime; as, to worship God aright.
a.
The right side; the side opposite to the left.
a.
Situated or being on the right; nearer the right hand than the left; as, the right-hand side, room, or road.
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.
adv.
In a right manner.
imp. & p. p.
of Dight
imp.
of Hight
superl
Having light; not dark or obscure; bright; clear; as, the apartment is light.
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.
adv.
In a great degree; very; wholly; unqualifiedly; extremely; highly; as, right humble; right noble; right valiant.
a.
Straight; direct; not crooked; as, a right line.
a.
Formed by right lines; rectilineal; as, a right-lined angle.
a.
Fit; suitable; proper; correct; becoming; as, the right man in the right place; the right way from London to Oxford.
a.
That which is right or correct.
v. t.
To cause to fight; to manage or maneuver in a fight; as, to fight cocks; to fight one's ship.
a.
Containing a right angle or right angles; as, a right-angled triangle.
p. p.
of Hight
v. t.
To get sight of; to see; as, to sight land; to sight a wreck.