If you are given values for two sides of an oblique triangle and an angle opposite one of them, how would you arrive at the values of the missing parts? Will this result in a unique triangle?
207719
you need to use the cosine rule.\n\nA^2 = B^2 + C^2 - 2BC*cos(a)\n\nwhere Capitals are the lengths of sides, and lower case is an angle opposite the side of the corresponding letter.
516743
Hi. Don't you hate these? OK you have an unknown angle. Call it a. You have a complement, c, which is 90-a. c=3a-10. Any help?
123163
There is no possible way that a triangle has a pair of parallel sides. In a pyramid, if the base is rectangular then the opposing sides of the base will be parallel but I assume that by triangular pyramid you mean the base is a triangle and each wall is a triangle...then nothing is parallel to anything.
172941
you may be dealing with "right" triangles, but you don't identify the angle that is 90, so your question is bout impossible to answer. this type of question usually involves  \na squared + b squared = c squared (a^2 + b^2 = c^2) where a and b are the 'legs' of the triangle in question. (the two 'legs' of a right triangle make the 90 degree corner) :)
258336
The answer is C\nwell, one side's length of a triangle should be shorter than the other 2's plus (2 sides plus should be longer than one side)\nthen: 3x+4+8x+2>6x-1\n      8x+2+6x-1>3x-4\n      6x-1+3x+4>8x+2\n--> x>-7/5\n    x>3/11\n    x>-1\nThus, the answer should be x>3/11\n:)
373102
They don't have values, they are operations, which means each one tells you to do something different (and shame on your teacher for not explaining this to the class BEFORE having you do them on your calculator). \n\nYou always have to have right triangles when dealing with these three trig functions (that's what sine, cosine and tangent are, trig functions). They are each ratios, which means a comparison of two numbers. Sine means to take the length of the opposite side (the side opposite the angle you're measuring) and put that number in a fraction as the numerator, then in the denominator put the length of the hypotenuse of the triangle. So for short, sine means "opposite over hypotenuse." Similarly, cosine means "adjacent over hypotenuse" and tangent means "opposite over adjacent." The adjacent side is the side forming the angle that is NOT the hypotenuse (this is really difficult to explain without being able to draw you a picture). My students called it SOHCAHTOA for short to remember them all.\n\nI'll try and walk you through an example as best I can...Draw an isoceles right triangle (which means the triangle has one right angle and two 45 degree angles). Since it's isoceles, the two sides that are NOT the hypotenuse must be the same length. So let's say those two sides each have a length of 1. If you do the pythagorean theorem (a squared plus b squared equals c squared) you'll get that the length of the hypotenuse is equal to the square root of 2, or approximately 1.414. Did you draw the pictures and label all the parts? \n\nNow pick one of those 45 degree angles and circle it. Let's calculate the sine of 45 degrees, WITHOUT using a calculator. Using that angle you chose, find the length of the opposite side (the side of the triangle that isn't touching the angle at all). It's 1 right? So put that in a fraction as the numerator, the number on top. Sine means opposite over hypotenuse, so in the denominator we need the length of the hypotenuse, which is the square root of 2 or 1.414. So your equation now says....\n\nsin 45=1/1.414\n\nOn your calculator, punch in 1 divided by 1.414 and you'll get the number 0.70721....\n\nMake sure your calculator is in degree mode, if it's not you'll get the wrong answer, it's a very common mistake!\n\nNow punch in sin 45 and hit enter. What number do you get? 0.70710....\n\nThe reason the two numbers are different is because we rounded the length of the hypotenuse. If we'd actually used the square root function on our calculators and typed in the square root of 2 instead of the decimal, they would have been exactly the same number. \n\nAnd it doesn't matter what the lengths of the sides of the triangles are, as long as they're right triangles. IF YOU DON'T HAVE RIGHT TRIANGLES THOUGH, YOU CAN'T USE THESE FUNCTIONS. So be careful. But that's all the sine, cosine and tangent represent. They are the ratios of the side lengths of right triangles. \n\nHere's a final example. The tangent of 51 degrees (tan 51) equals 1.23489..... That means that in a right triangle with a 51 degree angle, if you take the length of the side opposite the 51 degree angle and divide it by the length of the side adjacent to that angle (remember, tangent means "opposite over adjacent"), then you'd get 1.23489....\n\nI hope that helped. Good luck! I'm sorry I couldn't draw you a picture.
278634
Memorize that for any triangle having sides of length a, b, and c and angle C opposite side c,\n\nc^2 = a^2 + b^2 - 2abcos C .\n\nNote that for C = 90 degrees where cosine of 90 degrees is zero, the rule reduces to the pythagorean theorem.
555946
Actually the only way it would be possible is if you use Elliptic or Riemannian geometry, and would require a manifold.  A representation of such a construct would be similar to drawing a 4 dimensional shape in 3 or even 2 dimensions.\n\nEuclidian geometry doesn't allow triangles with a sum of all angles to be greater than 180 degrees.
448134
in a right triangle (any triangle with a 90deg angle), the hypotenuse is opposite the 90 angle.  The other two are proportional:  the smaller side is opposit the smaller angle, the (next) larger side is opposite the (next) larger angle.\n\nThe sum of the squares of both sides will equal the square of the hypotenuse.\n\nFor any integer n which is greater than 2, then a^n + b^n = c^n has no solutions in non-zero integers a, b, and c\n\nsin of an angle = opposite side/hypotenuse\ncos of an angle = adjacent side/hypotenuse\ntan of an angle = opposite side/adjacent side\n\nSOHCAHTOA\n\nthat's all you ever need to know to get through basic trigonometry.
339660
There's not enough information to answer the question. We need to know at least one angle as well as the length of two sides.
291604
A circle has 360 degrees. Now imagine that from the icosagon you can make 20 equally-sized triangles. The angle made by each triangle is 360/20=18 degrees. The other two angles of each triangle are both 81 degrees.\n\nThe basic formula for the area of a triangle is 1/2 base x height. How do we find these? Well, imagine that from each of the 20 triangles we make two additional right triangles. In doing this we know several things:\n\n-The hypotenuse is equal to 6.5 cm (the radius).\n-The angles of the smaller triangle are now 9 degrees, 81 degrees, and 90 degrees.\n-The sine of 9 degrees is equal to the opposite side divided by the hypotenuse. If we multiply this value by 6.6 we get the length of the opposite side ("1/2 base").\n-The sine of 81 degrees multiplied by 6.5 gives us the "height".\n-Once you compute each value (1/2 base and height) you multiply them by each other and you get the area of the triangle.\n-Multiply the area of that triangle by 20, since you have 20 of them. Voila.
444617
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.
612569
Here's simply why:\n\n2 isosceles triangles are not always similar. The common angle for an iso triangle is 45-45-90. Other isosceles triangles have angles 20-20-140, or 70-70-40, etc (2 angles are the same and all three add up to 180).\n\nFor equilateral triangles, they are always similar. All equalleral triangles have the angles 60-60-60, no matter what.
436234
multiply the tangent of the given angle by the known side as long as it's not the sloping side (i.e. the hypotenuse). You will need a scientific calculator to do this. I am assuming of course that you are dealing with a right triangle. This will give you the other side of the triangle. Example:\n\nlets say you have side A of a right triangle and an angle of 30 degrees and A = 10. Take your scientific calculator press 30 and then the tan button depending on the type of caculator you have. Now multiply that result by 10 and you will get side B.\n\nSide C is found by A^2 + B^2 = C^2. take the square root for your answer.\n\nNow if the given angle is opposite the given side. Just calculate the angle of the given side by adding the given angle to 90 degrees and subtract the result from 180, and then multiply the tangent of the new new angle by the given side.\n\nTheoretically you can check the answer by multiplying the new side by the tangent of the new angle. You should in theory get the given side. But my trig is so rusty I may have forgotten more than  you will ever know. good luck.
186357
From your question, we know the 3 points of the triangle are:\n(0,0), (0,y) and (x, y).\n\nThis points us to the fact that the right angle is at point (0,y).\n\nHence, area A of triangle is given by the product of base and height divided by 2. Therefore, we have:\n\n Area A of triangle = 1/2 [base.height]\n                    = 1/2 y.x\n\nWe are told y = x2, therefore:\n Area A of triangle = 1/2 y.x\n                    = 1/2 x3 (read as half x-cube)
473113
Sorry, but your question doesn't make sense.  Maybe you mean the midpoint of one of the sides of a right triangle.
429052
Best to plot this on a piece of graph paper; "+i" is  to the right' , "+j" is upwards, "-i" is to the left, "-j" is downwards, all with respect to the origin.\n\n1. Draw the vectors on the graph paper. "u" is in the second quadrant (i is neg and j is pos). "v" is in the fourth quadrant, with (i is pos, j neg) . There are two answers to this question, since you could go from u to v or from u to v in the opposite direction. I always take the angle from zero to "u" and add it to the angle from 0 to "v".  For "u", the tangent of the angle to the vertical axis is 1/4, then angle = 14%. So the angle from zero degrees to the vert axis = 90, and "u"s angle from zero degrees is 90 + 14 = 104 degrees. For "v", the tangent of the angle to the horizontal axis is 4/3 = 1.333.. and the angle = 53 degrees. Therefore the angle from "u" to "v" is 104 + 53 = 157 degrees. (the other answer is 360 degrees - 157 degrees = 203 degrees if you rotate in the other direction).\n\n2. Again use graph paper. 240 degrees is 30 degrees less that 270 degrees (the vertical axis, down) draw a line 10 graph units long. It will be in the third quadrant where i and j will both be negative. At this point you can use a polar to rectangular converter, or do it by hand. By hand: the i side of the triangle formed with the down axis can be found by saying sin(angle) = i/10, and cos(angle) = j/10. The angle is 30 degrees (from vert downwards). so sin(30) = 0.5, and, cos(30) = 0.866; thus i= 0.5 and j = 0.866 (ignoring pos/neg). Since the vector is in the third quadrant, both i and j are negative.\nAnswer = -0.5i -0.866j\n\nHope this helps!