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?
134802
any combinations of sides and angles 3 or more will give you what you need.
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.
121903
Bob, I used to enjoy your show before you started doing all those really expensive houses.  Then, of course, you left.\n\nOh, well.\n\nDon't you know, Bob, that isosceles triangles don't have "right sides?"  An isosceles triangle has two "legs" of equal length.  If it is a right isosceles triangle, the side opposite the right angle is called the hypotenuse.\n\nSay hi to Norm for me!
253965
You have to have a right triangle.\nThen you figure out which is side is opposite or adjacent from the angle you need.
55588
The trigonometric identities have as their primary purpose to simplify calculations.  For example, why evaluate 2sinxcosx when you can evaluate sin2x.\n\nAs for the applications, oblique triangles are used in surveying and mapping.  For example, suppose you want to know your distance from an object on the opposite side of a river.  You can mark off a line of a fixed distance, say 100ft.  Then, go to the opposite ends of the line and use a transit to measure the angle between the object and the line you measured.  You can now determine all three sides with this information.
209753
The cosine laws apply to triangles which are NOT right angled. I think you have maybe read that wrong:\n\nhttp://www.themathpage.com/aTrig/law-of-sines.htm\n\ngives you a full guide to using the cosine laws to solve problems like these.
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.
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.
464777
okay. so. there's a special set of rules for a 30-60-90 triangle.\n\nthe sides are proportional to each other by the ratio \n\nx : v/( 3)x : 2x\n\nwhere the v/ is the square root.\n\nthat means that the greatest angle corresponds to the greatest length.\n\nbecause the longest side is 7.5 meters, that means that is 2x.\n\ndivide by two for x, and that is the 30* length. (because its the smallest angle, therefore is opposite the smallest length)
411756
Start by drawing a picture of this.  Draw a right triangle.  I put the right angle at the bottom left.  Then draw an arbitrary line from the upper left vertex down to the base.  This separtes the large right triangle into a smaller right triangle and what I will call the "outer triangle."  This gives you the 1000 Jim moved; it's to the right of where the line intersects the base.  I called this leg a.  I drew in the angles I was given, and labeled all of the line segments.  The hypotenuse of the large right triangle is b, the hypotenuse of the smaller right triangle (also the only unlabeled leg of the outer triangle) is c, and the vertical leg of the right triangle is d.  d is the height of the escarpment.  I named the angles after the sides they face.  So the 10 degree angle is C, the 32.5 degree angle is D, and angle A is opposite leg a, and is an acute angle in the outer triangle.  Since I was given angle D, I could find its supplement, B, which is an obtuse angle in the outer triangle, opposite leg b.  B = 180 - D = 180 - 32.5 = 147.5.  Since the sum of angles in a triangle is 180, and I know C and B, I can also find A = 180 - B - C = 180 - 147.5 - 10 = 22.5.\n\nNow that I know every angle in the outer triangle and the length of one leg, a, I can use the law of sines.  The law of sines says that a / sin(A) = b / sin(B).  Rearranging, b = a*sin(B) / sin(A) = 1000*sin(147.5) / sin(22.5).  Now look at the larger right triangle.  You know the length of the hypotenuse, b, and you know the angle C opposite the unknown d (I called it C because it is also opposite leg c in the outer triangle.).  By trigonometry, d = b*sin(C) = b*sin(10), where we use b from above.
634161
The two smaller sides must always add up to more than the largest side (otherwise you can't make a triangle).  Since the sides must be *integer* sides, the only valid triangle is 2, 6 and 7.\n\nStated another way, here are the combinations:\n2-3-7, impossible triangle (try connecting the 2 and 3 sides together...)\n2-4-7, impossible triangle (try connecting the 2 and 4 sides together...)\n2-5-7, straight line, not a triangle\n2-6-7, valid triangle\n\nSo there is only one combination (2-6-7) that makes a triangle when x is an *integer* greater than 2 and less than 7.
195617
If the shape is a quadrilateral, the measures of its opposite angles WOULD add up to 180 degrees.  This is because the measure of an inscribed angle (an angle with vertex on the circle) is half the measure of its intercepted arc.  Between the two opposite angles, their combined arc is the whole circle which measures 360 degrees.  So the sum of the inscribed angles is half of that, or 180.
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:)
315582
Pick an angale, not the 90 degree angle and call it Theta.  The short side that forms this angle is called the x side of the triangle and the long side that forms this angle is the hypotenuse or 'r'.  The third side is called the opposite side or 'y'.\n\n\n.... /|\n..../.|\n.../..|\n../...|\n./....|\n/___|  Bottom is x, slanting side is r, and right side is \n          the y side.  The angle at the bottom left is Theta.\n\n\nSin(Theta) will = y/r\nCos(Theta) will = x/r\nand\nTan(Theta) will = y/x side.\n\nThis all presumes you don't already know 2 of the sides.  If you know 2 sides already, you use the pythagorean thm.\n\nExampe: Theta = 30 degrees, r = 10 feet, what are the others?\n\nSin(Theta) = y/r  and Sin(30 degrees) happens to be 1/2.\n\nso, 1/2 = y/10.  Solving for y you get y=5.
634140
Brian gave you the answer, but he didn't explain it thoroughly.\n\nPlace your vector at the origin of an x and y plane.  The x and y axes are perpendicular, so you can use the Pythagorean formula to get the magnitude which is the length of the hypotenuse of the right triangle formed by the points (0,0), (10,0), and (0,8). sqrt(10^2+8^2)\n\nNow you need direction which is the angle between the x axis and the vector. Since you have solved for all three lengths of the triangles sides, you can use any inverse trig function to find the angle.  Brian chose tangent.\n\nGood work, Brian!
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.
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?