one more pythagorean theorm help?
411199
a^2 + b^2 = c^2\n8^2 + 5^2 = c^2\n64 + 25 = c^2\n89 = c^2\n\nc = about 9.434miles
1028326
1 - A is enough because with the lengths of 2 sides you can use pythagoras' theorem to work out the length of the other
759539
Where c is the hypotenuse, and a and b are legs of the triangle:\nc² = a² + b² --- Pythagoren Therom\nc² = (12)² + (20)² --- Replace what you know...\nc² = 144 + 400 --- Find 12² and 20²...\nc² = 544 --- Add them together...\nc = √544 --- Square root of 544 equals c\nc ≈ 23.32"
497748
In rt triangle ABC with B= 90degrees (draw figure)      \nIf C is theta, cosC=7/8(ignoring sign)\ni.e., BC = 7, CA = 8 (in simplest terms)\nusing pythagoras theorem, AB= sqrt(15)\n \nsince C=theta is in the second quadrant tan C will be negative\n\nso tan C = AB / BC \n\n  tan C= - { sqrt(15) } / 7\n\ntan(theta) = -0.5533
42660
One. \n\nThis relation is really just Pythagoras' theorem, hiding in a new form. Recall:\n\nH^2 = A^2 + B^2 \n\nThat is, the square of the hypotenuse H is the sum of the squares of the other two sides A and B, for a right triangle with sides A, B and hypotenuse H.  \n\nOf course, A=H*cosx and B=H*sinx for some angle x, so that \n\nH^2= (H^2)*(sinx*sinx + cosx*cosx)\n\nleading to the result:\n\n1=sinx*sinx + cosx*cosx\n\nThis result also is nicely connected to the simple fact that \n\nx - x = 0 \n\nbecause \n\nexp(i*x)=cosx + i*sinx and\nexp(-i*x)=cosx -i*sinx\n\nwhere i=sqrt(-1). \n\nThen multiplying these two, \n\nsinx*sinx + cosx*cosx=exp(i*x)*exp(-i*x)=\nexp(i*[x-x])=exp(0)=1
303035
If the triangle is a right triangle, you can find the other side by Py's Th and then by the formula,(A=1/2bh).\nIf it is not, you should know the angle they make each other or an adjacent angle. Only if, you can find the area by sine laws or cosine laws.
918358
theorm of Pythagorus states that if one of the angle of triangle is right angle{90degrees} than the hypotenuese square{the side opposite to right angle} is egual to the sum of squares of the sides forming the right angle \ni.e. (Hyp)square =one side square + second side square \n a2=b2+c2
890883
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.
28789
Errata corrige to the last answer: the pythagorean triple is 15,20,25 and not 12,15,25.\n\nHope this helps
352673
Make right triangles with the height as one leg, a radius (segment from center of base to one of its vertices) as the other leg, and lateral edge as the hypotenuse.  The radius will equal the length of the base edge as it's a side of an equilateral triangle.  So 10^2 + 15^2 will equal lateral edge squared.\n\nSlant height would be the hypotenuse of a right triangle with legs of the pyramid's height, and the apothem (distance from center of base to midpoint of a side.)  You can get the apothem from Pythagorean theorem from the right triangle formed by half a base edge, a radius, and the apothem.  Then use the apothem in another Pythagorean theorem to get slant height.\n\nLateral area = 6 times the area of any one triangle.  Each triangle's area is 1/2 times 10 times slant height.\n\nVolume = 1/3 (area of base)(height).  The area of the base is 1/2 (apothem)(perimeter).\n\nThose are the steps.  Hope you can figure them out from this typing!
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!
1039593
A Pythagorean triple consists of three positive integers a, b, and c, such that a^2 + b^2 = c^2. Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k. A primitive Pythagorean triple is one in which a, b and c are coprime.\n\nThe name is derived from the Pythagorean theorem, of which every Pythagorean triple is a solution. The converse is not true. For instance, the triangle with sides a = b = 1 and c = √2 is right, but (1, 1, √2) is not a Pythagorean triple because √2 is not an integer. Moreover, 1 and √2 don't have an integer common multiple because √2 is irrational.\n\nThere are 16 primitive Pythagorean triples with c ≤ 100:\n(3, 4, 5) (20, 21, 29) (11, 60, 61) (13, 84, 85)\n(5, 12, 13) (12, 35, 37) (16, 63, 65) (36, 77, 85)\n(8, 15, 17) (9, 40, 41) (33, 56, 65) (39, 80, 89)\n(7, 24, 25) (28, 45, 53) (48, 55, 73) (65, 72, 97)
17334
Geometric -- multiplying the previous term by 4
1000630
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 :)
791994
First distance: Pythagorean Theorem is a squared + b squared = c squared.  So (2*2) + (3*3) = ???  Then find the square root of ??? \n\nThen the bearing: We first need to find the measure of angle A.  Since we know the length of all 3 sides, any of the SohCahToa formulas work.  Tangent is easiest here.  tan(A) = opposite/adjacent (length of opposite leg divided by length of adjacent leg).  tan(A) = 3/2.  Use the tan-1 key (probably will require shift key).  \n\nWe know the first leg of the trip is south which represents 180 degrees.  So add the found angle to 180 degrees.  (Draw it out, it should make sense.)
655583
The Pythagorean Theorem states that, in a right triangle, the sum of the squares of the lengths of the two sides which form the right angle is equal to the square of the length of the third side.\n\nThis is commonly stated as A^2 + B^2 = C^2, where A and B represent the lengths of the two sides which form a right angle, and where C represents the length of the other side.
1066472
The Pythagorean Theorem says that if you have a right triangle, then a squared + b squared = c squared.  The converse says that if you have a triangle in which a squared + b squared = c squared, then your triangle must be a right triangle.