What is the hypotenuse of a right triangle if one side is equal to 45 and the other side is equal to 74?
606740
c^2 = a^2 + b^2, where c = hypot\nc^2 = 45^2 + 74^2\nc = 86.6 or sqrt(7501)
980809
4 rules\n1.two sides and the included angles of the two triangles equal\n2.2 angles and a side of one triangle equal to 2 angles and a side of theothrtriangle\n3.3 sides of one equal tothe three sides of theother\n4.in 2 right angled triangles if the  hypotenuses and a side of each are equal
882750
Listen to the first guy.\nThe distance on the y axis is 1 ((-5)-(-4)) and on the x axis it is 3 ((-3)-0).\nThis gives you a right angles triangle with sides of 3 & 1. \nUnder Pythagoras theoem the sum of the squares is equal to the square of the hypoteneuse so\n1^2 + 3^2 = 10.\nTherefore the distance is the square root of 10.
421239
since this starts as a square.  when we place the diagonal line from the bottom right corner to the upper left corner we end up with two right triangles.  This is the perfect set up to use the Pythagorean theorem, which states "the square of the hypotenuese is qual to the sum of the squares of the base and height. you may have seen it as \n       h^2 = x^2 + y^2\nwe started with a square so we know the base (x) and height (y) are each 7 sq rt 2.\nsquare the values then add them together.  this will give you that diagonal's square. ****remember to take the sqrt of the answer to find the length of the diagonal.
406591
Switch your calculator from degrees (DEG) to radians (RAD). That should do the trick. \nHere are some quick trig rules you need to know:\nIn radians just remember that pi is 180 degrees. Pi/3 is 60 degrees, pi/2 is 90, pi/4 is 45 degrees and so on. \nIn a unit circle, the hypotenuse is always 1.\nSin is always the far side away from the angle (the vertical side). We call that the opposite side.\nCos is always the adjacent side (or horizontal side).\nIn a right triangle with angles 60 and 30, the shortest side is always 1/2 the hypotenuse, so in a unit triangle, it is just 1/2. You can use the pathagorean theorem to find that the longer side is the square root of (3/4), or (sqrt(3))/2.\nIn a right triangle with angles 45 and 45, the opposite and adjacent sides are equal, and we can use the pathagorean theorem to find that the sides are the square root of (1/2), or 1/(sqrt(2)).\n\n1. Sin 1/3 pi. This is the same as sin pi/3 which is a 60 degree angle. If you draw the triangle on a unit circle you would see that the opposite side is the longer side of a 90/60/30 triangle. We have seen above that the length is (sqrt(3))/2.\n\n2. Cos pi. Easy. pi is 180 degrees, so draw the unit circle. You see that it is just a striaght horizontal line going the other way so the answer is -1.\n\n3. cos pi/4 is a 45 degree angle. We know from above that both sides have to be 1/(sqrt(2)).\n\n4. sin pi/4. Same as #3.\n\n27. What is 315 degrees? Well draw your unit circle. Go, 90, then to 180, then to 270, then go 45 more degrees and you will end up at 315 degrees. Draw your triangle. We know that the hypotenuse is 1, so the coordinates will simply be, (cos 315, sin 315). Cos 315 is just a 90/45/45 triangle in the bottom right quadrant so the adjacent side is positive. The opposite is negative, so you end up with coordinates (1/(sqrt(2)), -1/(sqrt(2))). Do the same to solve the last question youeself.
158369
A 3-4-5 right triangle represents a triangle satisfying the Pythagorean Theorem where 5 is the hypotenuse and the other sides have the dimensions 3 and 4 (feet, inches, meters, whatever). Say you're building a foundation with a corner (or anything that needs to be square-90 deg at the corner).  If you measure off 3 ft form the corner in one direction, make a mark and 4ft in the other and make another mark, the distance between your marks (hypotenuse) better be 5 ft or the corner is not square.
837883
Draw a picture of the triangle formed to see that the side opposite the angle is 24 and the side adjacent is k, with 25 being the hypotenuse.  Sine = opp. leg/hyp. which is 24/25\nCosine = adj. leg. / hyp. = k/25\n\nIf you need to, you can find k using the Pyhhagorean Theorem\n(k squared = 25 squared - 24 squared), keeping in mind it can be positive or negative.
899919
16.72 inches squared.\n\n\nDivide an equilateral triangle into two equal right triangles (meaning, draw the height).  The right triangles will have angles of 30, 60, 90, right (an equilateral triangle has 3 60 degree angles)?\n\nThe ratio of the sides in such a right triangle (the smallest leg being a) is a:a(sq(3)):2a, where 2a is the hypotenuse and a(sq(3)) is the other leg.\n\nThe "other leg" in this case is the height.  So a, half of the length of the side of the whole equilateral triangle, is 5.382/sq(3).\n\nMultiply this by 2 to get the whole length of the side.  We have our base and height.\n\n\nThe area of an equilateral triangle is 1/2bh.  b=2(5.382)/sq(3)\nh=5.382\n\nPlug those in and you get 16.72.
1126492
Use pythagorean theorem.\n\n3^2 + 7^2 = hypotenuse (diagonal) squared\n\n9 + 49 = x^2\n\n58 = x^2\n\nsquare root of both sides  diagonal is = 7.61577  feet\n\n(or 7 feet 7.4 inches)
1104008
This forms a right triangle.  You can use the pythagorean theorem to find L.\nThe hypotenuse is 3L - 2, and the legs are L and 2L + 2\n(3L-2)^2 = L^2 + (2L+2)^2\n9L^2 - 12L + 4 = L^2 + 4L^2 + 8L + 4\n9L^2 - 12L + 4 = 5L^2 + 8L + 4\nSubtract 4 from each side.\n9L^2 - 12L = 5L^2 + 8L \nMove everything to one side.\n4L^2 - 20L = 0\nFactor\n4L(L-5) = 0\nL = 0 or L = 5\nThe height can't be zero; therefore, L = 5\ntan(x) = L/(2L+2)\ntan(x) = 5/(10+2)\nx = arctan(5/12)\nx = 22.619864948\nx = 23
273778
The lengths of a right triangle are a^2 + b^2 = c^2 (Pythagorean theorem).  For 6, 7, 8, this would mean that 36 + 49 = 64, which is false.  For 10, 15, 20 you would need 100+225 = 400, also false.\n\nThe one common ration that works is 3, 4, 5  (9+16 = 25).  Multiples also work, such as 15, 20, 25 (225 + 400 = 625).
264806
For a right triangle, a^2+b^2=c^2 where a & b are the legs and c is the hypoteneuse.\n\nSo,\n\nc^2 = 8^2+9^2\nc^2 = 64+81\nc^2 = 145\n\nThe square root of 145 is just over 12, so the answer is D.
217108
You have a right triangle with legs a and b, and hypotenuse c.\na+b=8\nc=6\n\na^2 + b^2 = c^2 = 36\n\nSquare both sides of a+b=8\na^2 + 2ab + b^2 = 64\n\nSubtract previous equation:\n\n2ab = 64 - 36 = 28\n\nab = 14\n\n(1/2)*ab = 7\n\nArea = 7.
518832
The hypotenuse is closely associated with the right triangle. In the right triangle, the hypotenuse is the longest side. The Pythagorean Theorem is a^2 + b^2 = c^2, which is (leg^2 + leg^2 = hypotenuse^2). a and b are both legs of the triangle and c is the hypotenuse
579919
Draw the triangle with the 20 degree angle.  Put a dot on the hypotenuse to represent the object.  Its mass goes straight down from the spot (gravity).  A perpendicular to the hill through the point represents the resultant.  The horizontal vector connects the bottom of the mass vector to the bottom of the resultant (perp.) vector making a 20-70-90 right triangle.  Tan (20) = horiz/vert (vert = mass) \nso horiz = mass times tan(20)
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.
42862
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