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Longest side of a right-angled triangle, the side opposite of the right angle
In geometry, a hypotenuse is the side of a right triangle that is opposite to the right angle. It is always the longest side of the triangle. The other
Hypotenuse
Relation between sides of a right triangle
right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of
Pythagorean_theorem
Fundamental trigonometric functions
side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that of the hypotenuse. For an angle θ {\displaystyle
Sine_and_cosine
Triangle containing a 90-degree angle
turn or 90 degrees). The side opposite to the right angle is called the hypotenuse (side c {\displaystyle c} in the figure). The sides adjacent to the right
Right_triangle
Area of geometry, about angles and lengths
the angle to the hypotenuse. sin A = opposite hypotenuse = a h . {\displaystyle \sin A={\frac {\textrm {opposite}}{\textrm {hypotenuse}}}={\frac {a}{h}}
Trigonometry
Optical illusion
13x5 if it were, because what appears to be the hypotenuse is bent. In other words, the "hypotenuse" does not maintain a consistent slope, even though
Missing_square_puzzle
Polygonal curve made from right triangles
with one leg being the hypotenuse of the prior right triangle and the other leg having length of 1; the length of the hypotenuse of this second right triangle
Spiral_of_Theodorus
Relationship between two figures of the same shape and size, or mirroring each other
side. RHS (right-angle-hypotenuse-side), also known as HL (hypotenuse-leg): If two right-angled triangles have their hypotenuses equal in length, and a
Congruence_(geometry)
Right triangle with a feature making calculations on the triangle easier
smallest ratio of the hypotenuse to the sum of the legs, namely √2/2. and the greatest ratio of the altitude from the hypotenuse to the sum of the legs
Special_right_triangle
Length of a line segment
outer square root converts the area of the square on the hypotenuse into the length of the hypotenuse. In terms of the Pythagorean addition operation ⊕ {\displaystyle
Euclidean_distance
Mathematical memory aids
for instance SOH-CAH-TOA in English: Sine = Opposite ÷ Hypotenuse Cosine = Adjacent ÷ Hypotenuse Tangent = Opposite ÷ Adjacent One way to remember the
Mnemonics_in_trigonometry
Integer side lengths of a right triangle
the problem of finding equal products of a non-hypotenuse side and the hypotenuse, ( a 2 − b 2 ) ( a 2 + b 2 ) = ( c 2 − d 2 ) ( c 2 + d 2 )
Pythagorean_triple
five-pointed white stars and two half stars, top and bottom, along the hypotenuse of the triangle. The three points of the triangle stand for the three
Flag of Bosnia and Herzegovina
Flag_of_Bosnia_and_Herzegovina
Theorem about right triangles
relation between the altitude on the hypotenuse in a right triangle and the two line segments it creates on the hypotenuse. It states that the geometric mean
Geometric_mean_theorem
Collection of proofs of equations involving trigonometric functions
a h {\displaystyle \sin \theta ={\frac {\mathrm {opposite} }{\mathrm {hypotenuse} }}={\frac {a}{h}}} cos θ = a d j a c e n t h y p o t e n u s e = b
Proofs of trigonometric identities
Proofs_of_trigonometric_identities
Hypotenuse of right triangle from its sides
binary operation on the real numbers that computes the length of the hypotenuse of a right triangle, given its two sides. Like the more familiar addition
Pythagorean_addition
Welding technique
the hypotenuse. The toes of the weld are essentially the edges or the points of the hypotenuse. The face of the weld is the outer visual or hypotenuse that
Fillet_weld
Perpendicular line segment from a triangle's side to opposite vertex
vertex angle. In a right triangle, the altitude drawn to the hypotenuse c divides the hypotenuse into two segments of lengths p and q. If we denote the length
Altitude_(triangle)
Side of a right triangle
right angle". The side opposite the right angle is the hypotenuse. In the context of the hypotenuse, the catheti are sometimes referred to simply as "the
Cathetus
Prime number congruent to 1 mod 4
the hypotenuse of a primitive Pythagorean triangle. For instance, the number 5 is a Pythagorean prime; 5 {\displaystyle {\sqrt {5}}} is the hypotenuse of
Pythagorean_prime
Functions of an angle
which are the trigonometric functions. In the following definitions, the hypotenuse is the length of the side opposite the right angle, opposite represents
Trigonometric_functions
Mathematical proof technique using contradiction
and hypotenuse a 2 {\displaystyle a^{2}} also would have integer sides including a square leg ( b 2 {\displaystyle b^{2}} ) and a square hypotenuse ( a
Proof_by_infinite_descent
Mathematician (c. 940-1000)
or Snell's law. The inner hypotenuse of the right-angled triangle shows the path of an incident ray and the outer hypotenuse shows an extension of the
Ibn_Sahl_(mathematician)
Measuring instrument in metalworking
chosen to be a whole number (for ease of later calculations) and forms the hypotenuse of a triangle when in use. When a sine bar is placed on a level surface
Sine_bar
On triangles inscribed in a circle with a diameter as an edge
and it is on its hypotenuse. The converse of Thales's theorem is then: the circumcenter of a right triangle lies on its hypotenuse. (Equivalently, a
Thales's_theorem
Inverse functions of sin, cos, tan, etc.
( opposite hypotenuse ) = arccos ( adjacent hypotenuse ) . {\displaystyle \theta =\arcsin \left({\frac {\text{opposite}}{\text{hypotenuse}}}\right)=\arccos
Inverse trigonometric functions
Inverse_trigonometric_functions
Relation between sine and cosine
right triangles in the figure, the ratio of its horizontal side to its hypotenuse is the same, namely cos θ. The elementary definitions of the sine and
Pythagorean trigonometric identity
Pythagorean_trigonometric_identity
Index of articles associated with the same name
the hypotenuse have the sum of squares of inverses of the integer legs equal to the square of the inverse of the integer altitude from the hypotenuse. Pythagorean
Sum_of_squares
Straight line segment that passes through the centre of a circle
Two-dimensional Surface Plane Area Polygon Triangle Centers Altitude Hypotenuse Pythagorean theorem Circular Hyperbolic Spherical Quadrilateral Parallelogram
Diameter
Mathematical model of the physical space
triangle with legs a, b and hypotenuse c: a 2 + b 2 = c 2 {\displaystyle a^{2}+b^{2}=c^{2}} The area of the square on the hypotenuse equals the sum of the areas
Euclidean_geometry
Circle with radius of one
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 y satisfy the equation
Unit_circle
Five early C18 observatories in India
assembly of instruments, consisting of a gigantic triangular gnomon with the hypotenuse parallel to the Earth's axis. On either side of the gnomon is a quadrant
Jantar_Mantar
Relation between the side lengths and altitude of a right triangle
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. Then
Inverse_Pythagorean_theorem
Triangle in hyperbolic geometry
the angle divided by the hyperbolic sine of the hypotenuse. sin A = sinh(opposite) sinh(hypotenuse) = sinh a sinh c . {\displaystyle \sin A={\frac
Hyperbolic_triangle
Dissection puzzle
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 (hypotenuse 1/2
Tangram
Angle defining a position in an orbit
center of the ellipse, its adjacent side lying on the major axis, having hypotenuse a (equal to the semi-major axis of the ellipse), and opposite side (perpendicular
Eccentric_anomaly
Vector distance function
Comparison of Chebyshev, Euclidean and taxicab/Manhattan distances for the hypotenuse of a 3-4-5 triangle on a chessboard (represented by a king, an ant, and
Minkowski_distance
N-th root of the product of n numbers
line extending perpendicularly from the hypotenuse to its 90° vertex. Imagining that this line splits the hypotenuse into two segments, the geometric mean
Geometric_mean
Indian mathematician and astronomer (1114–1185)
length of the hypotenuse is denoted by c, and the lengths of the other two sides are denoted by a and b. Then he computes the hypotenuse of a right angled
Bhāskara_II
Distance measure in radar and radio electronics
with respect to that of the radar antenna. The slant range (1) is the hypotenuse of the triangle represented by the altitude of the aircraft and the distance
Slant_range
Geometric model of the physical space
Two-dimensional Surface Plane Area Polygon Triangle Centers Altitude Hypotenuse Pythagorean theorem Circular Hyperbolic Spherical Quadrilateral Parallelogram
Three-dimensional_space
Computation machine that uses continuously varying data technology
between the hypotenuse and the adjacent side. At any distance along the adjacent side, a line perpendicular to it intersects the hypotenuse at a particular
Analog_computer
Military air navigation system
aircraft. It provides the user with bearing and distance (slant-range or hypotenuse) to a ground or ship-borne station. It is, from an end-user perspective
Tactical air navigation system
Tactical_air_navigation_system
Perimeter of a circle or ellipse
Two-dimensional Surface Plane Area Polygon Triangle Centers Altitude Hypotenuse Pythagorean theorem Circular Hyperbolic Spherical Quadrilateral Parallelogram
Circumference
Triangle with at least two sides congruent
a right triangle, the median from the hypotenuse (that is, the line segment from the midpoint of the hypotenuse to the right-angled vertex) triangulates
Isosceles_triangle
Natural number
maximum right triangles laid edge-to-edge before one revolution is completed. The largest triangle has a hypotenuse of 17 . {\displaystyle {\sqrt {17}}.}
17_(number)
Type of metric geometry
45-90-45. The two legs of both triangles have a taxicab length 2, but the hypotenuses are not congruent. This counterexample eliminates AAS, ASA, and SAS.
Taxicab_geometry
Mathematical invariance under transformations
Two-dimensional Surface Plane Area Polygon Triangle Centers Altitude Hypotenuse Pythagorean theorem Circular Hyperbolic Spherical Quadrilateral Parallelogram
Symmetry
Mathematical metric
Comparison of Chebyshev, Euclidean and Manhattan ('taxicab') distances for the hypotenuse of a 3-4-5 triangle on a chessboard
Chebyshev_distance
Interference pattern
the four sides equal to d = p/sin α; (we have a right triangle whose hypotenuse is d and the side opposite to the angle α is p). The pale lines correspond
Moiré_pattern
Mathematical space with a notion of distance
Comparison of Chebyshev, Euclidean and taxicab distances for the hypotenuse of a 3-4-5 triangle on a chessboard
Metric_space
Method of drawing geometric objects
Two-dimensional Surface Plane Area Polygon Triangle Centers Altitude Hypotenuse Pythagorean theorem Circular Hyperbolic Spherical Quadrilateral Parallelogram
Straightedge and compass construction
Straightedge_and_compass_construction
Natural number
greater than 1, in two ways, 85 = 92 + 22 = 72 + 62. the length of the hypotenuse of four Pythagorean triangles. a Smith number in decimal. The radix of
85_(number)
1951 song by Tom Lehrer
as the Hypotenuse. A fourth recording was made in 1966 when Songs by Tom Lehrer was reissued in stereo, with Doris Day playing the Hypotenuse. In 1957
Lobachevsky_(song)
Study of meaning in language
example, the profile of the word hypotenuse is a straight line while the base is a right-angled triangle of which the hypotenuse forms a part. Cognitive semantics
Semantics
Transparent optical element with flat, polished surfaces that refract light
cemented together) Various thin-film optical layers can be deposited on the hypotenuse of one right-angled prism, and cemented to another prism to form a beam-splitter
Prism_(optics)
Triangle with integer side lengths
x, y and hypotenuse z can generate a Pythagorean triangle with an integer altitude, by scaling up the sides by the length of the hypotenuse z. If d is
Integer_triangle
Natural number
vertices, and 233 connected topological spaces with four points It is the hypotenuse of a primitive Pythagorean triple: 2332 = 1052 + 2082. Sloane, N. J. A
233_(number)
Staves carried by Moses's brother, Aaron, in the Torah
of an interior corner, the maximum staff length would be the hypotenuse of the hypotenuses of length v depth and depth v height, or 2.5 2 + 1.5 2 + 1.5
Aaron's_rod
Cradle of civilization in North Africa
were aware, for example, that a triangle had a right angle opposite the hypotenuse when its sides were in a 3–4–5 ratio. They were able to estimate the area
Ancient_Egypt
Mathematical space with two coordinates
Two-dimensional Surface Plane Area Polygon Triangle Centers Altitude Hypotenuse Pythagorean theorem Circular Hyperbolic Spherical Quadrilateral Parallelogram
Two-dimensional_space
American comedy horror film series
Zero and a fourth film was revealed to be in development at Indomina and Hypotenuse Pictures, with both films expected to shoot back-to-back. Texas Chainsaw
Cabin_Fever_(franchise)
Type of non-Euclidean geometry
Two-dimensional Surface Plane Area Polygon Triangle Centers Altitude Hypotenuse Pythagorean theorem Circular Hyperbolic Spherical Quadrilateral Parallelogram
Hyperbolic_geometry
Topological space of dimension zero
Two-dimensional Surface Plane Area Polygon Triangle Centers Altitude Hypotenuse Pythagorean theorem Circular Hyperbolic Spherical Quadrilateral Parallelogram
Zero-dimensional_space
Natural number
number. 5 is the first congruent number, as well as the length of the hypotenuse of the smallest integer-sided right triangle, making part of the smallest
5
Babylonian clay tablet of numbers in Pythagorean triples
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 was roughly 13 to 15 centuries
Plimpton_322
Unique positive real number which when multiplied by itself gives 3
across to make a right angle with one side, the right angle triangle's hypotenuse is length one, and the sides are of length 1 2 {\textstyle {\frac {1}{2}}}
Square_root_of_3
German mathematician (1826–1866)
Two-dimensional Surface Plane Area Polygon Triangle Centers Altitude Hypotenuse Pythagorean theorem Circular Hyperbolic Spherical Quadrilateral Parallelogram
Bernhard_Riemann
Type of measurement error
for a few example angles are: The error is equivalent to treating the hypotenuse and one of the other sides of a right-angled triangle as if they were
Cosine_error
Anatomical area located in the right atrium of human heart
coronary sinus orifice and the vestibule of the right atrium, and the hypotenuse is formed by the tendon of Todaro, which is often a continuation off the
Koch's_triangle
2014 film by Kaare Andrews
Michael P. Mason Music by Kevin Riepl Production companies Indomina Group Hypotenuse Pictures Voltage Pictures Distributed by Tiberius Film (Germany) Image
Cabin_Fever:_Patient_Zero
Mathematical tree of integer right triangles
having the property that they can be respectively the two legs and the hypotenuse of a right triangle, thus satisfying the equation a 2 + b 2 = c 2 {\displaystyle
Tree of primitive Pythagorean triples
Tree_of_primitive_Pythagorean_triples
Sanskrit term for hearing
or "the ear." Depending on context, shravana can mean 'the ear', 'the hypotenuse of a triangle', 'the act of hearing', 'study', 'fame', 'glory', 'that
Shravana_(hearing)
Surface landmark of knee
Bryant's triangle (or iliofemoral triangle), which is mapped out thus: the hypotenuse of the right angled triangle is a line from the anterior superior iliac
Bryant's_triangle
Rational right triangles cannot have square area
right triangles in which the two legs of one triangle are the leg and hypotenuse of the other triangle. More abstractly, as a result about Diophantine
Fermat's right triangle theorem
Fermat's_right_triangle_theorem
Shape with five sides
depicted below the circle. Using Pythagoras' theorem and two sides, the hypotenuse of the larger triangle is found as 5 / 2 {\displaystyle \scriptstyle {\sqrt
Pentagon
Flat tool used in carpentry to mark right angles and calculate angles
the base of a roof (the plate). This number gives the unit line length (hypotenuse) of the common rafter per twelve inches of horizontal distance (run).
Steel_square
Infinitely detailed mathematical structure
Two-dimensional Surface Plane Area Polygon Triangle Centers Altitude Hypotenuse Pythagorean theorem Circular Hyperbolic Spherical Quadrilateral Parallelogram
Fractal
Unique positive real number which when multiplied by itself gives 2
geometrically in another way. Let △ ABC be a right isosceles triangle with hypotenuse length m and legs n as shown in Figure 2. By the Pythagorean theorem,
Square_root_of_2
five-pointed white stars and two half stars top and bottom along the hypotenuse of the triangle. Botswana Botswana 2:3 September 30, 1966 George Winstanley
List of national flags of sovereign states
List_of_national_flags_of_sovereign_states
90° angle (π/2 radians)
and along the second side exactly four units in length, will create a hypotenuse (the longer line opposite the right angle that connects the two measured
Right_angle
Number, approximately 1.618
{\displaystyle BC} half the length of A B {\displaystyle AB} . Draw the hypotenuse A C {\displaystyle AC} . Draw an arc with center C {\displaystyle
Golden_ratio
Non-Euclidean geometry
Two-dimensional Surface Plane Area Polygon Triangle Centers Altitude Hypotenuse Pythagorean theorem Circular Hyperbolic Spherical Quadrilateral Parallelogram
Elliptic_geometry
Relationship between two lines that meet at a right angle
Two-dimensional Surface Plane Area Polygon Triangle Centers Altitude Hypotenuse Pythagorean theorem Circular Hyperbolic Spherical Quadrilateral Parallelogram
Perpendicular
Spacing between equally-spaced square numbers
possible for the pair of legs of a Pythagorean triangle to be the leg and hypotenuse of another Pythagorean triangle. A proof was eventually given by Pierre
Congruum
Branch of mathematics
Two-dimensional Surface Plane Area Polygon Triangle Centers Altitude Hypotenuse Pythagorean theorem Circular Hyperbolic Spherical Quadrilateral Parallelogram
Algebraic_geometry
Circle that passes through the vertices of a triangle
a right triangle, the circumcenter always lies at the midpoint of the hypotenuse. This is one form of Thales' theorem. For an obtuse triangle (a triangle
Circumcircle
Type of reflective prism
used almost exclusively for images appearing at infinity. If the flat hypotenuse surface of a Dove prism is cut into a roof shape, the result is an Amici
Dove_prism
Property of geometry, also used to generalize the notion of "distance" in metric spaces
triangles, the triangle inequality specializes to the statement that the hypotenuse is greater than either of the two sides and less than their sum. The second
Triangle_inequality
Type of Chinese dumpling
initially folding the wonton skin into a right triangle, each end of the hypotenuse is pressed against the middle of opposite sides, creating an impression
Wonton
Property of all triangles on a Euclidean plane
triangle, sin δ = opposite hypotenuse = c 2 R , {\displaystyle \sin {\delta }={\frac {\text{opposite}}{\text{hypotenuse}}}={\frac {c}{2R}},} where R
Law_of_sines
Number whose square is a given number
the right triangle with legs 1 and x {\displaystyle {\sqrt {x}}} has a hypotenuse of x + 1 {\displaystyle {\sqrt {x+1}}} . Constructing successive square
Square_root
Property of a mathematical space
Two-dimensional Surface Plane Area Polygon Triangle Centers Altitude Hypotenuse Pythagorean theorem Circular Hyperbolic Spherical Quadrilateral Parallelogram
Dimension
Concept in geometry
Two-dimensional Surface Plane Area Polygon Triangle Centers Altitude Hypotenuse Pythagorean theorem Circular Hyperbolic Spherical Quadrilateral Parallelogram
Area_of_a_circle
Unsolved problem about sums of powers
Pythagóras triangle A, where d is hypotenuse, a and b are sides c2 = e2 + f2 Pythagóras triangle B, where c is hypotenuse, e and f are sides if you sum both
Prouhet–Tarry–Escott_problem
Suburb of Melbourne, Victoria, Australia
Williamstown Road, in the south by Somerville Road, with Geelong Road as the hypotenuse. Kingsville was the original name for the entire West Yarraville region
Kingsville,_Victoria
Equation of the form 1/a + 1/b = 1/c
themselves) equals the reciprocal of the square of the altitude from the hypotenuse. This holds whether or not the numbers are integers; there is a formula
Optic_equation
1975 English language song from Germany
Angle-Angle-Side), through a song playfully naming "RHS" (Right-angle-Hypotenuse-Side, the fifth evidence for proving congruent triangles) which lines
Fly,_Robin,_Fly
Basic concepts of algebra
c^{2}} , representing the square of the length of the side that is the hypotenuse, the side opposite the right angle, is equal to the sum (addition) of
Elementary_algebra
Geometric space with four dimensions
Two-dimensional Surface Plane Area Polygon Triangle Centers Altitude Hypotenuse Pythagorean theorem Circular Hyperbolic Spherical Quadrilateral Parallelogram
Four-dimensional_space
HYPOTENUSE
HYPOTENUSE
HYPOTENUSE
HYPOTENUSE
Boy/Male
Tamil
Tusharkanti | தà¯à®·à®¾à®° காஂதி
Lord Shiva
Girl/Female
Irish
Long haired.
Boy/Male
British, English
From the Roe-deer Brook
Boy/Male
Arabic
Hill; High Place
Boy/Male
Czechoslovakian
Peaceful glory.
Boy/Male
Australian, Chinese
Kingly
Girl/Female
Tamil
Treasure
Boy/Male
Hindu, Indian, Marathi
Future
Male
German
German form of Arabic Ahmed, ACHMED means "praiseworthy."
Boy/Male
German
Ruler
HYPOTENUSE
HYPOTENUSE
HYPOTENUSE
HYPOTENUSE
HYPOTENUSE
n.
Same as Hypotenuse.
n.
Alt. of Hypothenuse