right triangle

mathematics

Also known as: right-angled triangle

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July 13, 2026

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A right triangle is a triangle that contains one right angle (90 degrees). The sides that form the right angle are called legs, and the side opposite the right angle is called the hypotenuse. The Pythagorean theorem is a fundamental property of right triangles, stating that the square of the hypotenuse's length is equal to the sum of the squares of the lengths of the two legs (a² + b² = c²). Trigonometric functions like sine, cosine, and tangent relate an angle in a right triangle to the ratios of its side lengths, which are useful in fields such as engineering and navigation.1234

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East Asian mathematics
Problems involving right triangles
…to solve various problems on right triangles such as the following: “Given the base, and the sum of the height and of the hypotenuse, find the height and the hypotenuse.” Other algorithms are given for determining the diameter of an inscribed circle and the side of an inscribed square.
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…to solve various problems on right triangles such as the following: “Given the base, and the sum of the height and of the hypotenuse, find the height and the hypotenuse.” Other algorithms are given for determining the diameter of an inscribed circle and the side of an inscribed square.
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tangent
In trigonometry of a right triangle, the tangent of an angle is the ratio of the side opposite the angle to the side adjacent. The value of the tangent (ratio) depends only on the size of the angle, not on the particular right triangle used to compute it.
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In trigonometry of a right triangle, the tangent of an angle is the ratio of the side opposite the angle to the side adjacent. The value of the tangent (ratio) depends only on the size of the angle, not on the particular right triangle used to compute it.
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