In a 30-60-90 Triangle, what is the length of the hypotenuse?
110612
2x\nwhen the side opposite the 30 degree angle is x\nand the side opp the 60 degree angle is x(root3)
422360
A triangle is 180 degrees... so 28 + 58 = 86. so now solve this: 180-86=....94!! Tah Dah!
753210
The rope is the hypotenuse of the triangle you need to analyse so it's going to be sin60 or cos60 times 75N. An easy way to decide which: as a test, consider if the angle were 90. The horizontal component would be 0. Is sin90 or cos90 = 0? Cos, right? So the component of the force parallel to the floor is cos60 times 75N.
555107
MY guess is that your trying to find the Hypotenuse of a triangle.  Thus A^2+B^2=C^2 or in this case H^2+W^2 = C^2, 25 + 196 = C^2, 221 = C^2, C = 14.86.  Missing side is 14.86.
1086757
If you realize that this would make a 30-60-90 triangle the answer is really easy.  The ratio of the sides of a 30-60-90 triangle are 1:2:sqrt(3)  In your example, that means that the height off the ground would be half the length of the bed.  Half of 86" is 43", so it will be 43" inches off the ground.\n\nYou can also use the sin(30) formula, but sin(30) is simply 0.5, so you get the same answer:\n\nn = 86 sin(30)\nn = 86 * 0.5\nn = 43\n\nSo the answer either way is 43 inches off the ground.
997563
You're looking for the angle that has a sine of 1/2.\nDrawing a triangle representing this is very helpful.  You will see that it is a 30-60-90 triangle.  \nIf you can find it in degrees, then you can convert it to radians by multiplying it by pi/180.\nsine(30) = 1/2\n30 degrees = 30(pi/180) = pi/6
798165
If it's a right triangle, use the Pythagorean Theorem.\n\na^2 + b^2 = c^2\n\n\nA and B are the legs (the ones that touch the right angle), C is the hypotenuse which is opposite the right angle.\n\n10^2 + x^2 = 26\n\n100 + x^2 = 676\n\nx^2 = 576\n\nx = 24
966174
a triangle with angles 30, 60,90\nhas sides in ratio 1: (SR 3) : 2\nThe equilateral triangle can be formed from\ntwo 30,60,90 triangles.\neach of those can be formed from 3 smaller 30,60,90 triangles\nso the equilateral triangle can be formed from six 30,60,90 triangles.\nIf radius of circle is 1 unit,\neach of the six small 30,60,90 triangles has \nsides (1/2) ((SR 3)/2) 1\nso the equilateral triangle has side SR(3) units\nso if the equilateral triangle has side x, the circle has radius x /(SR(3)),\nand the circle circumference is 2 pi x /((SR 3))
535960
The speed has no part in the solution, as it is the same for all three paths. So, you draw a triangly with legs 2.25 and 3 in lenght. the solution is the lenght of the hypotenusa formed. the answer is 3.75 min.
187445
hypotenuse=36cm=c\none leg=20cm=b\nother leg=?=a\n\nFormula:\na^2=c^2-b^2\na^2=36^2-20^2\na^2=1296-400\na^2=896\na=square root of 896.\nby using a calculator extracting the square root, we arrive at an answer of\na=29.9332590941 or 30cm\n\nThe other leg's measure is 30cm by the Pythagorean Theorem.
155406
By definition,hypotenuse is the side opposite the right angle. So it has to be a right angled triangle.
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.
736929
I think I'd start with 9 isosceles triangles.\n\nEach angle at the apex is 360 divided by 9 degrees\n\n=40degrees.\n\nThe other two angles are equal, so subtract 40 degs from 180 degs and halve what's left.\n\nEach base angle of the triangle = 70 degs.\n\nYou already have 40degs and the side opposite it (0.80m)\n\nSo you can use a over sinA = b over sinB to find the other two (equal) sides of the isosceles triangle.\n\nNow drop a perpendicular from the apex of the isosceles triangle to the (middle of) its base, forming two right angled triangles.\n\nEach of these triangles is half of the isosceles triangle.\n(remember the base of the right angled triangle is half the 0.80m)\n\nNow you can use \n\nsin = opp/hyp,  cos = adj/hyp,  tan = opp/adj to find the length of the perpendicular height.\n\nNearly there!\n\nArea of a triangle = half the base times perpendicular height \n\nWhen you've worked this out for one of the isosceles triangles, you just have to remember back in line one, that you are finding the area of 9 identical triangles, so you multiply the area of one by 9 to get the area of the nonagon.\n\nThis uses lots of fairly sinple steps, which you should be able to remember in an exam.  PS don't try to remember the order of the steps we used here, just have confidence that when you start, the solution will unfold for you.  If you wanted to practice, try it in a week with a different polygon!
943973
Tangent 25° 56' 30" = cot (90 - A)\n\n89 59 60\n25 56 30\n- - - - - - -\n\n64 3 30\n\nCotangent 64 degrees 3 minutes 30 seconds\n\nThe answer is. The complemenary angle of tangent 25° 56' 30" is cotangent  64° 3' 30 "\n\n- - - - - - - - - - - -s-
739053
#30 is 58.88.  Area = pie*(diameter/2) squared\n#38 is 900.  Area of triangle = .5 base*height\n\n#44 is 73,950\n\nCircumference = Pi X Diameter\n\nSo 3.14 X 2.33 ft. (14 in tireX 2 to convert to diameter)/(12 to convert to feet)=7.14 feet per tire revolution and the trip is 100 miles (5280 ftx100) or 528,000 ft.  528,000 ft/7.14= 73,950 tire rotations to complete the trip.
669681
1.  Area of rt triangle whose leg is 6ft and whose\n    hypotenuse is 10ft?\n\n    Area = 24 sq. ft.  \n\n  Explanation:\n\n    First we need to find the other leg's length...\n    Using Pythagorean Theorem,\n    \n    c**2=a**2+b**2 \n       \n    where c is the hypotenuse, a is one leg, and \n    b is the other leg.\n\n    So, 100 = 36 + b**2;  b**2 = 100-36 = 64; therefore b=8.\n    Now, Area = 1/2(base*height) since the base is one leg\n    (we'll say it is a) and the height is the other leg \n    (therefore we'll name it b) \n    the Area = 1/2(8*6) = 1/2(48)= 24 sq. ft.\n\n2.   The hypotenuse is approx. 4.9 meters.\n    \n  Explanation:\n     \n     Using Pythagorean Theorem: c**2=a**2+b**2 we find that\n     c**2 = (3.5)(3.5) + (3.5)(3.5)\n     c**2 = 12.25 + 12.25\n     c**2 = 24.25\n     c = sq. rt. (24.25)\n     c = 4.9244 meters\n     hypotenuse is approx. 4.9 meters.\n\n3. hypotenuse is approx. 20 inches long.\n\n  Explanation: Area = 1/2(x)**2 \n               where x is length of one leg.\n\n     x**2 = 2*Area;\n     x**2 = 2*98\n     x**2 = 196\n     x = sq. rt. (196)\n     x = 14 inches\n\n     Now, to find length of hypotenuse, we use the\n     Pythagorean Theorem:\n\n     c**2 = a**2 + b**2; since a=b this can be rewritten so\n     c**2 = 2(a)**2\n     c**2 = 2(14)**2 -- Remember 14 is the length of a leg.\n     c**2 = 2(196)\n     c**2 = 392\n     c    = sq. rt. (392)\n     c = 19.7989\n     c is approx. 20 inches long.\n\n\n4.   The researcher will climb approx. 10 meters \n     to reach the crack.\n\n   Explanation:\n      \n      Using the Pythagorean Theorem: c**2 = a**2 + b**2\n      If we set a = 24, then c**2 = (24)**2 + b**2,\n      but we also know that c + b = 36 \n      which means c = 36 - b.\n\n      So to solve for this we need to set\n      (36-b)**2 = (24)**2 + b**2\n      1296-72b + b**2 = (24)**2 + b**2\n      1296 - 72b = (24)**2\n      1296 - 72b = 576\n      -72b = 576 - 1296\n      -72b = -720\n         b = -720/-72\n         b = 10 \n\n      And now we have our 10 meters the researcher \n      must climb to reach the crack in the tree.\n\n\n6.    Approximately a 42 inch stick is the longest stick\n      that will fit in a box that is 24 in X 30 in X 18 in.\n\n  Explanation:\n\n      First use Pythagorean Theorem to find the diagonal\n      inside the rectangle of 24 in X 30 in.\n\n      c**2 = (24)**2 + (30)**2\n      c**2 = 576 + 900\n      c**2 = 1476\n      c = approx. 38.418 in. -- we will call it 38 in.\n\n      Now, use Pythagorean Theorem to find the diagonal\n      inside the "new and invisible" rectangle that is \n      38 in. X 18 in.\n\n      c**2 = (38)**2 + (18)**2\n      c**2 = 1476 + 324\n      c**2 = 1800\n      c = sq. rt. (1800)\n      c is approx. 42.43 in.  \n      \n      We will call "c" 42 inches long.
1053705
The legs of a triangle have the lengths 5 and 12.  What is the  length of the hypotenuse? Answer: 13\n\nThe legs of a triangle have the lengths 7 and 11.  What is the  length of the hypotenuse? Answer: sqrt(170)\n\nThe length of the hypotenuse of a triangle is 25.  One of the legs has length 24.  What is the length of the other leg? Answer:7\n\nThe length of the hypotenuse of a triangle is 15.  One of the legs has length 12.  What is the length of the other leg? Answer: 9\n\nThe length of the hypotenuse of a right isosceles triangle is 8.  What is the length of the two legs? Answer: 4sqrt(2)