Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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 [Broken] 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).​
     
    Last edited by a moderator: May 3, 2017
  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
     
    Last edited by a moderator: May 3, 2017
  16. Oct 22, 2008 #15

    Hey Tim,
    Were you talking about this construction??
    http://img147.imageshack.us/img147/1702/diagqp4pq9.jpg [Broken]
    Please help me yar!
     
    Last edited by a moderator: May 3, 2017
  17. Oct 22, 2008 #16

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    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.
     
    Last edited by a moderator: May 3, 2017
  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
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook