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Triangle Inequality

  1. Oct 20, 2008 #1
    Hi guys!!
    There is one question after which I have been for hours. I need to prove that:
    tan C > b/c
    in an acute angled triangle.
    I cannot get started.
    I tried to convert b/c to sin B/sin C but no useful results. .. and so on.
    Please help me as soon as possible!
     
    Last edited: Oct 20, 2008
  2. jcsd
  3. Oct 20, 2008 #2

    tiny-tim

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    Hi ritwik06! :smile:

    That's obviously not true :frown:

    try it for B = C < 45º.
     
  4. Oct 20, 2008 #3
    Hey tim,
    HI!!
    Actually, if you read the question carefully, its said that the triangle is acute angled. If B=C<45
    => A>90
     
  5. Oct 20, 2008 #4

    tiny-tim

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    oops!

    oops! :redface:

    let me try again …

    try it for C < 45º and B > 90º - C.

    have i got it right this time? :rolleyes:
     
  6. Oct 20, 2008 #5
    Re: oops!

    Hey tim,
    thanks a lot for trying this. :smile:
    The actual thing is that I have to prove that
    c tanC / b > 1
    can you help me?
     
  7. Oct 21, 2008 #6

    tiny-tim

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    Use the sine rule! :rolleyes:

    What do you get? :smile:
     
  8. Oct 21, 2008 #7
    sin A/a= sin B/ b= sin C/c
    But how does this help????
     
  9. Oct 21, 2008 #8

    tiny-tim

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    Oh come on! :rolleyes:

    That's not using the sine rule. :frown:
     
  10. Oct 21, 2008 #9
    From sine rule I get ;
    c tan C/b = (c*c sin B)/ (b*b cos C)

    What next??
    Did you get the answer sir? I mean were you able to prove it? :smile:
    Thanks a lot. But I think my brain's week- I still cant see through it. Please help me further tim.
    Ritwik
     
    Last edited: Oct 21, 2008
  11. Oct 21, 2008 #10
    I have noticed that:
    B+C>90
    B>90-C
    as both angles are less than 90
    sin B> cos C
    But still, I dont get what I want to prove.
     
  12. Oct 21, 2008 #11

    tiny-tim

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    Yes, that's good! :smile:

    Are you sure the question isn't to prove b tanC / c > 1 ?
     
  13. Oct 21, 2008 #12
    the question is to prove that (c tan C)/b > 1 !!!!
    Is it difficult?
     
    Last edited: Oct 21, 2008
  14. Oct 21, 2008 #13

    tiny-tim

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    This is the PM you sent me while the PF server was offline:
    Ritwik, in this forum, you should always state the full question. :frown:

    The picture, http://img510.imageshack.us/img510/8586/diagqp4.jpg gives information that was not in any of your previous posts.

    You have wasted your time and mine by not giving the full question.

    Do not ever do that again. :mad:

    Hint: draw the line through AG perpendicular to AC and meeting BC at G (so AG is parallel to FB).​
     
  15. Oct 21, 2008 #14
    I am really very very sorry for that. I thought I had reached close enough to the answer, thats why I didn't type the whole question.

    Sir, Please be specific about which line are you talking about?
    I dont understand this:
    Hint: draw the line through AG perpendicular to AC and meeting BC at G (so AG is parallel to FB).

    Please re-read your statement. Are you talking about a perpendicular from point D on AC?? If, yes I have done it already. If no, Please specify clearly what constructions do you hint at.

    Sorry once again for that!
    Ritwik
     
  16. Oct 22, 2008 #15

    Hey Tim,
    Were you talking about this construction??
    http://img147.imageshack.us/img147/1702/diagqp4pq9.jpg
    Please help me yar!
     
  17. Oct 22, 2008 #16

    tiny-tim

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    No, that's the line through D parallel to FB.

    (it probably works in the end, but it would be complicated)

    It is much simpler to draw the line through A parallel to FB.
     
  18. Oct 22, 2008 #17
    SOLVED
    Thanks a lot tim for your efforts. I have solved this . Thanks a lot for the help!
    regards,
    Ritwik
     
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