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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.
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°).
In the following definitions, the hypotenuse is the side opposite to the 90-degree angle in a right triangle; it is the longest side of the triangle and one of the two sides adjacent to angle A. The adjacent leg is the other side that is adjacent to angle A. The opposite side is the side that is opposite to angle A.
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.
The hypotenuse c (which is always odd) is the sum of two squares. This requires all of its prime factors to be primes of the form 4n + 1. [16] Therefore, c is of the form 4n + 1. A sequence of possible hypotenuse numbers for a primitive Pythagorean triple can be found at (sequence A008846 in the OEIS).
The diagonal and sides referred to are those of a rectangle (oblong), and the areas are those of the squares having these line segments as their sides. Since the diagonal of a rectangle is the hypotenuse of the right triangle formed by two adjacent sides, the statement is seen to be equivalent to the Pythagorean theorem. [8]
In this way, this trigonometric identity involving the tangent and the secant follows from the Pythagorean theorem. The angle opposite the leg of length 1 (this angle can be labeled φ = π/2 − θ) has cotangent equal to the length of the other leg, and cosecant equal to the length of the hypotenuse. In that way, this trigonometric identity ...
The hypotenuse is a constant dimension—(100 mm or 10 inches in the examples shown). The height is obtained from the dimension between the bottom of one roller and the table's surface. The angle is calculated by using the sine rule (a trigonometric function from mathematics). Some engineering and metalworking reference books contain tables ...