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Equivalent equations and not equivalent answers?

  1. Sep 3, 2004 #1
    Ok, What do you do when two equations that should yield the same answer dont? For example when finding the area of a SSA triangle:
    A= 25 degrees
    side a = 100
    side b = 200

    Now, I know this triangle gives two possible answers but I am just concentrating on answer 1, when using the law of sines you get
    B= 57.6973 degrees
    which leaves C= 97.3027 degrees

    Now, if you use the equation:

    (a^2*sinB*sinC) / (2sinA) You get 9,958.48 inches^2

    But, if you use .5(a)(b*sinC) which should work also, you get 9,925.88 inches^2

    If these equations are equivalent then why do they give different answers? Is it just calculator rounding?
     
    Last edited: Sep 3, 2004
  2. jcsd
  3. Sep 3, 2004 #2

    Hurkyl

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    Have you tried using more accurate numbers? (e.g. B isn't exactly 58 degrees)
     
  4. Sep 3, 2004 #3
    Sorry, I just rounded a few numbers to make it easier to read, but using my ti-89 and using the numbers it gives me I still get equation
    1. = 9958.48 inches^2 and equation
    2. = 9918.88 inches^2
     
  5. Sep 3, 2004 #4

    Hurkyl

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    Have you tried using more accurate numbers? (e.g. B isn't exactly 58 degrees)
     
  6. Sep 3, 2004 #5

    HallsofIvy

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    I don't know that it is "calculator" rounding. Surely your calculator gives better than 2 digit accuracy: but it is reasonable for you to round to 2 digits: you were given A as 25 degrees: 2 digits accuracy. Of course, after you have done that, there is no point in expecting more than 2 digits accuracy in your answer: rounded to 2 digits, you get 9900 or, better, 9.9x103.
     
  7. Sep 3, 2004 #6
    The answers I gave in my second post are from using the exact numbers my calculator gave me to solve it. I just don't understand why two equations that should give the same answer dont? I sort of understand why 2 digit accuracy would follow through to my answer I guess, it just seems counterintuitive that two equivalent equations give different answers.
     
  8. Sep 3, 2004 #7

    Hurkyl

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    No they're not. You used 58 for B and 97 for C.



    It's not so bad once you get used to the idea. The + sign on your calculator really is something slightly different than the + sign you write in mathematical formulae.
     
  9. Sep 3, 2004 #8
    Sorry, I edited my first post to show that I used a more accurate answer than just 58 and 97 when getting my answers, I should have just done that in the first place but used rounded answers so my post would look nicer. But anyways, I think you guys have explained it well enough for me. It was just something I had noticed more than once in more than one kind of formula that always bothered me. Thanks
     
  10. Sep 4, 2004 #9
    Well, I hate to keep this thread going but I did a little test with Mathematica. I took all of my values to a precision of 100,000 decimal places and then computed the two answers. The answers I got of course where more precise than my calculator and gave me very similar results, they are the same down to somewhere around 25 or so decimal places. I just thought you guys would like to know, and thanks for the help.
     
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