given C= 61 degrees, a=55, and b=29 the area of the triangle.?
814915
Area = ½ ab SinC\n Area = ½(55)(29) Sin 61º\n Area = ½(1595) Sin 61º\n Area = 797∙5 Sin 61º\n Area = 797∙5(0∙874 619 707)\n Area = 697∙509 2165\n Area ≈ 697∙51 square units.
38263
5.196 (3 times root 3)\nDive the triangle into 3 equal triangles.  Then divide each one of those triangles into 2 triangles.  The hypotnuse of each triangle has a length of 2, and by trig. (it is a 30-60-90 triangle) the base has a length of the square root of 3 and the height is 1. Area of a triangle =(base times height)/2=(radical 3)/2.  There are 6 smaller triangles total, so multiply the area by 6=total area=3 times radical 3 (5.196)\nHope this helps, it would be a lot easier if I had a picture that I could post and it would make more sense.
471423
The area of the rectangle is:\n A of rectangle = L X W = 12 x 8 = 96 sq in\n\nThe area of the triangle is:\nA of triangle = 1/2 (A)(B) = 1/2 (A)(32 in) where A is the altitude to the base B of the triangle.\n\nsince both areas are equal:\n96 sq. in = 1/2(A)(32 in)\n96 sq. in = A (16 in)\nA = (96 sq. in)/16 in\nA = 6 inches
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
503124
first split the triangle in half. \nfind the height of the triangle (with the 12cm side as base)\n\n7^2 - 6^2 = (height)^2\nheight = 3.61\n\nUse formula\n\nArea = (0.5) (height)(base)\n     = (0.5) (3.61)(12)\n     = 21.66 cm squared
588642
a^2 + b^2 = c^2\n\nthis assumes right angles, a and b are the length and width, c is the diagonal
572270
triangle area = 1/2(height * width)\n\ncircle area = pi * radius^2
1167473
Here is the answer to your question (using the Pythagorean Theorem):  a^2 + b^2 = c^2, a and b are legs of the triangle, c is the hypotenuse.  So c = 26.\n\nso you have:  a^2 + b^2 = c^2\n                       a^2 + b^2 = 26^2\n                       a^2 + b^2 = 676\n                       \nNow, you need two squares that add up to 676.  The only squares that will work are 10 and 24.  So, here is what it looks like:\n\n                     10^2 + 24^2 = 26^2\n                     100 + 576 = 676\n                          676 = 676\nSince you get the same thing on both sides, you have the right answer.  This means that 10 and 24 are the lenglths of the other two sides of the triangle.\n\nHope this answers your question.\n\nChris (Math Teacher)
865942
b = 70sin55\n\nb = 57.34
926515
Let x be the length for the square and 14-x for the triangle.\n\nThe area of the square is (x/4)^2 = (x^2)/16.\n\nThe height of the triangle is sqrt(3)(14-x)/6 and the base of the triangle is (14-x)/3, so the area of the triangle is\n\n1/2 bh = [(14-x)/6] [sqrt(3)(14-x)/6] = (14-x)^2 sqrt(3)/36\n\nTotal area A = (x^2)/16 + (14-x)^2 sqrt(3)/36\n\nA = [9x^2 + 4(x^2 - 28x + 196) sqrt(3)] / 144\n\nA = [(9 + 4 sqrt 3) x^2 - (112 sqrt 3) x + (784 sqrt 3)] / 144\n\ndA/dx = [2(9 + 4 sqrt 3) x - (112 sqrt 3)] / 144 = 0\n\n(9 + 4 sqrt 3) x = 56 sqrt 3\n\nx = (56 sqrt 3) / (9 + 4 sqrt 3) = 6.0895 meters  (Answer)\n\nThe area of the square is 2.32 m^2.  The area of the triangle is 3.01 m^2, and the total area is 5.33 m^2.
644806
if the triangle is a regular triangle\n\na = (1/2)bh\n\na = (1/2)(6)(6 * sin60)\n\na = (1/2)(6)(3√3)\n\na = 9√3 = 15.588\n\n\nfor a regular polygon, \narea = (n*t^2) / (4*tan(π/n))\n\nwhere n = number of sides & t = length of side
1104391
The angles in a triangle add up to 180, so the answer is b. 40 degrees.
175713
Your question is too complicated to appreciate the math in it, which is supposed to be the real beauty in the first place. Anyway, I have tried figuring it out and come with equations. I do not even want to try and begin substitution and end up with more complications. I just thought once you saw the relation, you would throw those 10 points my way.\n\nAssuming a to be sides of the squares of the prism and b to be the length of the rectangles, we know that the sum of all dimensions is 14a+5b. Now I do not even want to get started why you brought it the story of the equilateral triangle. You can just say the sum  of the dimensions is 61. Anyway, since any side of the trianle, as it is equiangular hence equilateral, is twice 14a+5b and 122, the sum of the dimensions will be 61. So your first equation is 14a+5b=61\n\nYou know the volume of the prism is the length X width X heiht = a x a x b = (a^2)b This is equal to the surface area. The surface area is the sum of all the areas on the prism and that is a^2+4ab. (How about you calculate how that came up?)\n\nSo there is your second equation, (a^2)b = a^2+4ab So then from 14a+5b=61, express a in terms of b or the other way around and plug it into the second equation and experience brutal complications and figure out what the variables are. I think you know it is too easy to calculate each dimension and area after that.
689129
Each triangle on both sides of the diagonal is a right triangle.\n\nLet breadth = b\n\nSo, 12^2+b^2 = 13^2\n\nor b = sqrt(169-144) = sqrt(25) = 5\n\nSo, the area is 12*5 = 60
857682
The midpoint of A and B is (15+7)/2 = 11.\nIf C = 11 then AC =BC.\nTherefore AC < BC  for 11<C<15
698661
[Note: < denotes angle]\n\n<A + <B +<C = 180 \n(Because, in a triangle, sum of the angles is 180)\n\n<B + <C = 180 - <A\n<B + <C = 180 - 40\n<B + <C = 140.......(1)\n\nBecause this is an isosceles triangle, AB = AC,  the angles opposite the equal sides are equal (congruent), \ntherefore <B = <C ........ (2)\n\nSubstituting value of <B from (2) to (1), we get:\n\n<C + <C = 140\n\n2 * <C = 140\n\n<C = 140/2 = 70\n\n<C is the angle opposite line AB, which is 70 degrees.
628701
Area = 1/2 ac Sin B\n\nwhere a,b,c are the sides and A B C are the opposite angles. \nFrom the 10 sided figure you get an internal angle of 360/10 - 36 degrees so the other two angles are 180-36 all divided by 2 = 144/2 = 72 degrees.\n\nand the outside edge is 240/10 = 24\n\nSo using ac = 24 and Sin 36.. plug into the formula above.. this gives you the area of one triangle, then multiply by 10