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Altitude Proof

  1. Sep 26, 2004 #1
    Altitude Sum Proof

    Hi all,

    I have this problem that I have no idea where to start. It asks to prove for a triangle with altitudes h_a, h_b, and h_c, that

    [tex]\frac{1}{h_a} < \frac{1}{h_b} + \frac{1}{h_c}[/tex]

    Any idea how to begin this proof? I've tried all sorts of algebra, and utitlizing the Triangle Inequality, but I can't seem to reach this conclusion. Any help is greatly appreciated -- thank you! :)
     
    Last edited: Sep 26, 2004
  2. jcsd
  3. Sep 26, 2004 #2
    What do you mean by altitudes [tex]h_a h_b[/tex] and [tex]h_c[/tex]???

    The Bob (2004 ©)
     
  4. Sep 26, 2004 #3

    robphy

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    possible hint: "area"
     
  5. Sep 26, 2004 #4

    arildno

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    I'll upgrade that into a probable hint :wink:
     
  6. Sep 26, 2004 #5
    So the h_a, h_b and h_c are all angles???

    The Bob (2004 ©)
     
  7. Sep 26, 2004 #6

    arildno

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    No, they are heights:
    Let A be the area.
    Then a=A/h_a, b=A/h_b,c=A/h_c
    Using the triangle inequality for a,b,c yields the proposition.
     
  8. Sep 26, 2004 #7
    Sorry I didn't post sooner -- I figured it out on my own a little after I had posted, but didn't have time to post my solution. I used the method Arildno suggested.
    Thank you for your input, though! :)
     
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