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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).
Such a pair of sides may also be said to form an angle of zero. A triangle with a zero angle is impossible in Euclidean geometry for straight sides lying on distinct lines. However, such zero angles are possible with tangent circles. A triangle with one ideal vertex is called an omega triangle. Special Triangles with ideal vertices are:
For example, if one of the legs of a right angle has a length of 3 and the other has a length of 4, then their squares add up to 25 = 9 + 16 = 3 × 3 + 4 × 4. Since 25 is the square of the hypotenuse, the length of the hypotenuse is the square root of 25, that is, 5.
An exterior angle of a triangle is an angle that is a linear pair (and hence supplementary) to an interior angle. The measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it; this is the exterior angle theorem. [34]
The interior angle concept can be extended in a consistent way to crossed polygons such as star polygons by using the concept of directed angles.In general, the interior angle sum in degrees of any closed polygon, including crossed (self-intersecting) ones, is then given by 180(n–2k)°, where n is the number of vertices, and the strictly positive integer k is the number of total (360 ...
For example, the sine of angle θ is defined as being the length of the opposite side divided by the length of the hypotenuse. The six trigonometric functions are defined for every real number, except, for some of them, for angles that differ from 0 by a multiple of the right angle (90°). Referring to the diagram at the right, the six ...
A right-angled triangle where c 1 and c 2 are the catheti and h is the hypotenuse. In a right triangle, a cathetus (originally from the Greek word κάθετος, "perpendicular"; plural: catheti), commonly known as a leg, is either of the sides that are adjacent to the right angle. It is occasionally called a "side about the right angle".
The cosine of the larger of the two non-right angles is the ratio of the adjacent side (the shorter of the two sides) to the hypotenuse, , from which it follows that the two non-right angles are [1] θ = sin − 1 1 φ ≈ 38.1727 ∘ {\displaystyle \theta =\sin ^{-1}{\frac {1}{\varphi }}\approx 38.1727^{\circ }} and θ = cos − 1 1 φ ...