Equivalent equations and not equivalent answers?

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In summary, the conversation discusses two equations that should yield the same answer but give different results. It is suggested that the difference may be due to rounding errors or using less accurate numbers. The conversation also mentions the idea that the plus sign on a calculator may be slightly different from the one used in mathematical equations. A test using a more precise tool like Mathematica shows that the answers are very similar, differing only in the decimal places.
  • #1
mewmew
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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?
 
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  • #2
Have you tried using more accurate numbers? (e.g. B isn't exactly 58 degrees)
 
  • #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
 
  • #4
Have you tried using more accurate numbers? (e.g. B isn't exactly 58 degrees)
 
  • #5
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.
 
  • #6
Have you tried using more accurate numbers? (e.g. B isn't exactly 58 degrees)
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.
 
  • #7
The answers I gave in my second post are from using the exact numbers my calculator gave me to solve it.

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



it just seems counterintuitive that two equivalent equations give different answers.

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.
 
  • #8
Hurkyl said:
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.

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
 
  • #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.
 

1. What are equivalent equations?

Equivalent equations are two or more equations that have the same solution or solutions. This means that if you were to graph both equations, they would result in the same line or lines.

2. How do you know if two equations are equivalent?

To determine if two equations are equivalent, you can solve them using the same method (such as substitution or elimination) and compare the solutions. If the solutions are the same, then the equations are equivalent.

3. Can two equations have the same solution but not be equivalent?

Yes, two equations can have the same solution but not be equivalent. This can happen if one equation is a simplified version of the other, or if one equation has extraneous solutions that are not relevant to the other equation.

4. How do you use equivalent equations to solve a problem?

If a problem involves an unknown variable, you can create equivalent equations using the given information and then solve for the variable. This can help you find the solution or solutions to the problem.

5. What is the importance of understanding equivalent equations?

Understanding equivalent equations is important in solving mathematical problems and in higher level math courses. It allows you to manipulate equations and systems of equations in order to find solutions and make connections between different mathematical concepts.

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