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For example, a right triangle may have angles that form simple relationships, such as 45°–45°–90°. This is called an "angle-based" right triangle. A "side-based" right triangle is one in which the lengths of the sides form ratios of whole numbers, such as 3 : 4 : 5, or of other special numbers such as the golden ratio.
Inside, the triangle is depicted with all of its angles and side lengths. The right angle is marked as a small square. To the right of the 90° angle is another angle represented by an arc, and its measure, 45°, is written to the left of it. Atop the right angle is another angle symbolized by an arc, and its measure, 45°, is written below it.
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 fact that the triangle with these proportions is a right triangle follows from the fact that, for squared edge lengths with these proportions, the defining polynomial of the golden ratio is the same as the formula given by the Pythagorean theorem for the squared edge lengths of a right triangle: = +
[1] [2] [3] The triangle whose side lengths are 3, 4, 5 is a Brahmagupta triangle and so also is the triangle whose side lengths are 13, 14, 15. The Brahmagupta triangle is a special case of the Heronian triangle which is a triangle whose side lengths and area are all positive integers but the side lengths need not necessarily be consecutive ...
A right triangle with the hypotenuse c. In a right triangle, the hypotenuse is the side that is opposite the right angle, while the other two sides are called the catheti or legs. [7] The length of the hypotenuse can be calculated using the square root function implied by the Pythagorean theorem.
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The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the formula + =; thus, Pythagorean triples describe the three integer side lengths of a right triangle. However, right triangles with non-integer sides do not form Pythagorean triples. For instance, the triangle with sides = = and ...