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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.
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 length of the hypotenuse is thus the square root of 169, denoted , which equals 13. The Pythagorean theorem, and hence this length, can also be derived from the law of cosines in trigonometry. In a right triangle, the cosine of an angle is the ratio of the leg
In other words, a Pythagorean triple represents the lengths of the sides of a right triangle where all three sides have integer lengths. [1] Such a triple is commonly written (a, b, c). Some well-known examples are (3, 4, 5) and (5, 12, 13). A primitive Pythagorean triple is one in which a, b and c are coprime (the greatest common divisor of a ...
For the angle α, the sine function gives the ratio of the length of the opposite side to the length of the hypotenuse.. To define the sine and cosine of an acute angle , start with a right triangle that contains an angle of measure ; in the accompanying figure, angle in a right triangle is the angle of interest.
Automedian triangle, a triangle whose squared side lengths form an arithmetic progression, including the right triangle with side lengths :: Golden triangle , an isosceles triangle whose ratio of base to side length is the golden ratio.
Triangles have many types based on the length of the sides and the angles. A triangle whose sides are all the same length is an equilateral triangle, [3] a triangle with two sides having the same length is an isosceles triangle, [4] [a] and a triangle with three different-length sides is a scalene triangle. [7]
It is occasionally called a "side about the 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 other two sides". If the catheti of a right triangle have equal lengths, the triangle is isosceles. If they have different lengths, a distinction ...