A right triangle △ABC with its right angle at C, hypotenuse c, and legs a and b,
A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular, forming a right angle (1⁄4 turn or 90 degrees).
The side opposite to the right angle is called the hypotenuse (side in the figure). The sides adjacent to the right angle are called legs (or catheti, singular: cathetus). Side may be identified as the side adjacent to angle and opposite (or opposed to) angle while side is the side adjacent to angle and opposite angle
Every right triangle is half of a rectangle which has been divided along its diagonal. When the rectangle is a square, its right-triangular half is isosceles, with two congruent sides and two congruent angles. When the rectangle is not a square, its right-triangular half is scalene.
Every triangle whose base is the diameter of a circle and whose apex lies on the circle is a right triangle, with the right angle at the apex and the hypotenuse as the base; conversely, the circumcircle of any right triangle has the hypotenuse as its diameter. This is Thales' theorem.
The legs and hypotenuse of a right triangle satisfy the Pythagorean theorem: the sum of the areas of the squares on two legs is the area of the square on the hypotenuse, If the lengths of all three sides of a right triangle are integers, the triangle is called a Pythagorean triangle and its side lengths are collectively known as a Pythagorean triple.
The relations between the sides and angles of a right triangle provides one way of defining and understanding trigonometry, the study of the metrical relationships between lengths and angles.
A righttriangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular...
equal. Triangles can also be classified according to their internal angles, measured here in degrees. A righttriangle (or right-angled triangle) has one...
A special righttriangle is a righttriangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist...
the equilateral triangle as a special case. Examples of isosceles triangles include the isosceles righttriangle, the golden triangle, and the faces of...
^{1}} , and the triangle inequality expresses a relationship between absolute values. In Euclidean geometry, for righttriangles the triangle inequality is...
the three sides of a righttriangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to...
a right angle in a triangle is the defining factor for righttriangles, making the right angle basic to trigonometry. The meaning of right in 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...
positive integer k. A triangle whose side lengths are a Pythagorean triple is a righttriangle and called a Pythagorean triangle. A primitive Pythagorean...
equilateral triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triangle is also equiangular;...
geometric mean theorem or righttriangle altitude theorem is a relation between the altitude on the hypotenuse in a righttriangle and the two line segments...
A Kepler triangle is a special righttriangle with edge lengths in geometric progression. The ratio of the progression is φ {\displaystyle {\sqrt {\varphi...
In particular, the trigonometric functions relate the angles of a righttriangle with ratios of its side lengths. The field emerged in the Hellenistic...
. he has proved himself mathematician." A righttriangle with two equal legs is a 45-degree righttriangle, all of which are similar. The length of the...
The sine and cosine of an acute angle are defined in the context of a righttriangle: for the specified angle, its sine is the ratio of the length of the...
quadrantal triangle can be derived from those for a right-angled triangle. The polar triangle of a polar triangle is the original triangle. The cosine...
isosceles trapezoids, right kites, and regular polygons are cyclic, but not every polygon is. The circumcenter of a triangle can be constructed by drawing...
circle's circumference, then |x| and |y| are the lengths of the legs of a righttriangle whose hypotenuse has length 1. Thus, by the Pythagorean theorem, x and...
composed of righttriangles, placed edge-to-edge. It was named after Theodorus of Cyrene. The spiral is started with an isosceles righttriangle, with each...
The solution is particularly simple for skinny triangles that are also isosceles or righttriangles: in these cases the need for trigonometric functions...
a right isosceles triangle is a packing problem where the objective is to pack n unit circles into the smallest possible isosceles righttriangle. Minimum...
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...
point Fermat's righttriangle theorem Fuhrmann circle Fuhrmann triangle Geometric mean theorem GEOS circle Gergonne point Golden triangle (mathematics)...
side of a righttriangle opposite the right angle. It is the longest side of any such triangle; the two other shorter sides of such a triangle are called...
the Pythagorean theorem, which holds only for righttriangles: if γ {\displaystyle \gamma } is a right angle then cos γ = 0 , {\displaystyle \cos \gamma...
righttriangle, 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...
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