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As a consequence of the Pythagorean theorem, the hypotenuse is the longest side of any right triangle; that is, the hypotenuse is longer than either of the triangle's legs. For example, given the length of the legs a = 5 and b = 12, then the sum of the legs squared is (5 × 5) + (12 × 12) = 169, the square of the hypotenuse.
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".
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 International Phonetic Alphabet (IPA) can be used to represent sound correspondences among various accents and dialects of the English language. These charts give a diaphoneme for each sound, followed by its realization in different dialects.
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 ] Baudhāyana also provides a statement using a rope measure of the reduced form of the Pythagorean theorem for an isosceles right triangle :
The Pythagorean theorem: The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c). Although Pythagoras is most famous today for his alleged mathematical discoveries, [132] [207] classical historians dispute whether he himself ever actually made any significant contributions to the field.
In mathematics, sine and cosine are trigonometric functions of an angle.The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that ...
The following table shows the 24 consonant phonemes found in most dialects of English, plus /x/, whose distribution is more limited. Fortis consonants are always voiceless, aspirated in syllable onset (except in clusters beginning with /s/ or /ʃ/), and sometimes also glottalized to an extent in syllable coda (most likely to occur with /t/, see T-glottalization), while lenis consonants are ...