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Right angle triangle problem

  1. Dec 17, 2013 #1
    The number of degrees in one acute angle of a right-angled triangle is equal to the number of grades in the other; express both the angles in degrees.

    So I have found the following answers :

    810/17=47,05... degrees and 810/17=47,05... grades which gives 42,35... degrees

    Now, the real answer is the following :

    900/19=47,3... degrees and 900/19=47,3... grades which gives 42,63... degrees

    The only problem with my answer is the following :

    810/17degrees=900/17grades

    so : 900/17 grades+ 810/17 grades = 100,5.. grades (but for the rest, everything is fine, I get get 90 degrees perfectly and respect all conditions.)

    Would you count this as an error ???

    Here's what I did : (Help me see the error)

    x degrees= (x+x/9) grades

    x grades= (x-x/9) degrees

    so..

    x degrees+(x-x/9)degrees=90 degrees

    17x/9 degrees=90 degrees

    17x=810

    x=810/17 degrees

    By the formulaiton of the problem, we also have 810/17 grades

    Conversion

    810/17 degrees=(810/17+(810/17)/9) grades=900/17 grades

    and

    810/17 grades=(810/17-(810/17)/9) degrees= 720/17 degrees

    Can somebody tell me where I went wrong ??? (By the way, I see how to obtain the "real" answer, but I don't see why mine would be wrong ...)

    Thank you !
     
  2. jcsd
  3. Dec 17, 2013 #2
    Can you explain what the term "grades" means? I've never heard of that term and a Google search isn't showing any useful links.
     
  4. Dec 17, 2013 #3
  5. Dec 17, 2013 #4
    Thanks for the link! Took me a little bit, but if ##1^{\circ} = \frac{10}{9}^g##, then ##1^g = \frac{9}{10}^{\circ}##.

    ##1^{\circ} = (1 + \frac{1}{9})^g \implies x^{\circ} = (x + \frac{x}{9})^g##
    ##1^g = (1-\frac{1}{10})^{\circ} \implies x^g = (x-\frac{x}{10})^{\circ}##

    Basically, the fraction is supposed to have a denominator of 10, not 9.

    So you solve the equation ##x + x - \frac{x}{10} = 90##
     
  6. Dec 17, 2013 #5
    Oh,wow, I just noticed my error!(With the 10) Thank you ! Thats why I was getting a wrong answer !
     
  7. Dec 17, 2013 #6
    Yes, it's working ! Those are the times when I feel really ashamed of myself for doing stupid errors like this one -_____- Thank you agian!
     
  8. Dec 17, 2013 #7
    We've all been there, I assure you! :biggrin:
     
  9. Dec 18, 2013 #8

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    I am used to that being called "grads", not "grades". (And "gradian" is too easily confused with "radian".) There are 100 grads in a right angle so that it measures "percentage slope".
     
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