do u no the four Pythagoras's elemnets??
110464
I'm guessing with Earth, Water, Fire, and Wind (air).
618925
Integer solutions to the Pythagorean equation are called Pythagorean Triples. These are more interesting if they are primitive Triples, ie ones in which the 3 sides have no common factor. eg (3, 4, 5) is primitive but (6, 8, 10) is non-primitive.\n\nHere are three sequences of triples\n\n(3, 4, 5), (5, 12, 13), (7, 24, 25), (9, 40, 41) in which the two largest sides differ by 1. See if you can work out the next ones in the series.\n\n(8, 15, 17), (12, 35, 37), (16, 63, 65), (20, 99, 101), which the two largest sides differ by 2. See if you can work out the next ones in the series.\n\n(3, 4, 5), (20, 21, 29), (119, 120, 169). (696, 697, 985)  in which the two smaller sides differ by 1. This is how you can work out the next ones in the series:\n\ngiven (x, y, z) is a triple with this property (y-x = 1)\ncreate (X, Y, Z) as follows\n\nX = 2x + y + 2z \nY = x + 2y + 2z\nZ = 2x + 2y + 3z \n\nworking it through for (3, 4, 5) that leads to\nX = 6 + 4 + 10 = 20\nY = 3 + 8 + 10 = 21\nZ = 6 + 8 + 15 = 29\n\nworking it through for (119, 120, 169) that leads to\nX = 238 + 120 + 338 = 696\nY = 119 + 240 + 338 = 697\nZ = 238 + 240 + 507 = 985\n\nhave fun with numbers, good luck!
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Pythagoras’ Theorem \n"For any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.” \n\na2 + b2 = c2
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1)One leg of a right triangle is 12 cm long. The diference between the other two sides is 2 cm.\nFind the sides of the triangle. (Pythagorean Theorem)\n\nWhat we can take from this problem is that one LEG is 12 cm long, while the other LEG is unknown (we will call it X) and the HYPOTENUSE -- the longest side of a right triangle -- is also unknown (we will designate it X+2, since it differs 2 cm from the unknown leg).\n\nSetting up Pythagorean Theorem as always:\n\n "Leg squared" + "Leg squared" = "Hypotenuse squared"\n\n  12^2 + x^2 = (x+2)^2\n\nExpanding:\n\n  144 + x^2 = x^2 + 4x + 4\n\nCollecting like terms:\n\n  4x = 140\n\nDivide by 4:\n\n   x = 35\n\nThe unknown leg is 35 cm, while the hypotenuse is 37.  Thus, we can also call the triplet (12,35,37) a "Pythagorean Triple" (of which there are infinitely many!).\n\n\n2) The hypotenuse of a right triangle is 58 cm long. The diference between the other two sides\nis 2 cm. Find the sides of the triangle. (Pythagorean Theorem\n\nIn this case, we know the hypotenuse, but do not know the lengths of the legs.  For convenience, we will again use the expressions X and (X+2) for each side's length.\n\nBy P.T.:\n\n x^2 + (x+2)^2 = 58^2\n\nExpanding:\n\n x^2 + x^2 + 4x + 4 = 3364\n\nCollect like terms:\n\n 2 x^2 + 4x - 3360 = 0\n\nDivide by the GCF (2):\n\n  x^2 + 2x - 1680 = 0\n\nCan we factor this trinomial easily?  We could, if we knew integer factors of -1680 (one positive, one negative) that combine to make 2.\n\nLuckily, -1680 can be factored into -2*2*2*2*3*5*7, and these can be grouped into two sets:\n      2*3*7 = 42\n -2*2*2*5 = -40\n\nFactor:\n\n (x+42) (x-40) = 0\n\nAlthough two solutions come from these factors (-42 and 40), we may only consider the positive answer, since lengths of triangle's legs are always positive!\n\n Therefore, x=40 (Leg 1), and Leg 2 is 42 cm.
1066144
Without the knowledge of where point e is, this problem is insolvable.\n\nI suspect, however, from a brief diagramming session, that you will need to solve for the length of ab using the Pythagorean Theorem, and set up similar triangles.
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The Pythagorean Theorem can only be applied to Right Triangles only.\n\nIn a right triangle, the side opposite the 90 degree angle is called the HYPOTENUSE. The other two sides are called LEGS.\n\nTHEOREM:\nThe square of the hypotenuse is equal to the sum of the squares of the legs. \n\nEQUATION: Supposing,\nc = hypotenuse\na = first leg\nb = second leg\n\nThen:\n\nc^2 = a^2 + b^2\n\nThis is the conventional way of assigning the letters to the sides of the right triangle. However, if other letters will be assigned, then determine which letter will represent the hypotenuse so that its square can be placed on the left side of the equation. The others will be placed on the right side.
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U R RIGHTT..HOW DID YA GET IT..PLZ CAN YA EXPLAIN..I'VE BEEN TRYING THIS PROBLEM FROM A LONGTIME.EVEN DE CALCULATOR SAYS ITZ "4"..I KNOW DE CALCULATORS WRONG TOO..PLZZ DO EXPLAIN IT TO ME ASAP
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You **did** say that the Pythagorean Theorem was a given, right? I think that your INTENT is to prove the converse of the Pythagorean Theorem, right?\n\nLet x, y, and z be positive integers such that\nx^2 + y^2 = z^2.\nClearly z > x and z > y (otherwise either x^2 or y^2 must be less than zero; prove this for yourself if you must).\n\nLet x and y be the sides of a right triangle that form the right angle.\nThen, by the Pythagorean Theorem the length of the hypotenuse h is\nh = √(x^2 + y^2)\nh = √(z^2) . . . . . . . . (given equation above)\nh = z . . . . . . . . . . . (given z is positive) \n        \nTherefore, by side-side-side congruence, any triangle whose sides are of lengths, x, y, and z, where x^2 + y^2 = z^2, must be a right triangle with hypotenuse z.\n\n\nASIDE TO HOOD...: You are using the Pythagorean Theorem to prove the Pythagorean Theorem. Although the questioner's intent is not perfectly clear, I don't think the intent was to prove "if x, then x". If so there are easier ways to do so.
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Use the pythagorean Therym(?)\nThat is, well, here is an example:\nIf one leg of a right triangle is 6 units, and the other leg is 8 units, what is the legnth of the hypotenuse?\nthat is:\nleg 1=a, leg 2=b, and the hypotenuse = c\nThe hypotenuse always = c, it is the side parallel to the right angle of the triangle.\nthe pythagorean therym(?) is a^2(a squared)+b^2(b squared)=c^2(c squared)\na=6, b=8, and c=?\n6^2+8^2=c^2\n36 + 64= c^2\n100= c^2\nc=10^2\nso the missing side would b 10 units, just use that example for your problem, and remember, if you are trying to find the legnth of a leg, just plug in the one leg length that you have (this would be "a") and the hypotenuse(this would be "c") and subtract the square of "a" from "c". find the square root, and vua la, there you have it. hope that helps
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There are quite a few method for proving pythagoras theorem. I feel that easiest and neatest is by similarity of triagles ..\n\nproof 6 of the link
61592
There is actually a little controversy surrounding whether or not Pythagoras was actually the one who discovered the theorem, or if it was another of his associates, the Pythagoreans.  This website: http://www.geom.uiuc.edu/~demo5337/Group3/hist.html has some interesting history of other cultures illustrating an understanding of this, without expressing it in literal mathematical language.\n\nAs far as your second question, a great illustration can be found at http://mathforum.org/library/drmath/view/53937.html    The pythagorean theorem is actually a specific instance of the law of cosines, which is represented as a^2 = b^2 + c^2 - 2ab*cos(a).  As you can see, the equation only becomes the pythagorean theorem if 2ab*cos(a) = 0, which only happens if the angle is 90 degrees.
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Yes!!!!!!!!! Email me, and I'll try to shed more light on this. Parabolas are where my genius comes out :)
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B. 4, 5, 6.\n\nThe others are known Pythagorean triples, but not this one. 4^2+5^2 > 6^2\n41 > 36
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A pythagorean primitive is a triple in which their only common divisor is 1.\n\nFor example: 3,4,5 is a Pythagorean primitive and 6,8,10 is not.
60565
If I told you, you would get the answer correct, but would not have learned your trig assignment.\n\nHint:  Those tables in the back of the book are there for a reason!
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sure it does\n\nx^2-8x+4x-32\n\nx^2-4x-32\n\nRemember FOIL\nFirst Outer Inner Last
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Pythagoras Theorem asserts that for a right triangle with short sides of length a and b and long side of length c \na2 + b2 = c2 \n\nor c2-a2 = b2 \n\nhere is a link with all the necessary thing you have to know about this theorem . I hope it helps , just read it carefully and everything is going to be fine :)