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#1 Re: Help Me ! » Triangle related » 2005-12-12 05:59:20

Mathsy,
Thank you very much for the explanation, it really helped!

#2 Re: Help Me ! » Triangle related » 2005-12-11 13:43:59

Mathsy,
Many thanks indeed for your response. I think, I kinda lost touch with my math fundamentals (makes me sad sad ). It has been a while since I worked on math problems, and I encountered this problem while working on a location based service issue. I did not quite follow a small part of your response, I greatly appreciate if you can help me understand.

"I is at its biggest possible when the expression inside the arccos is at its smallest. This happens when h = j and i is at its maximum, so i = 0.5(h+j) = h, because h = j."

I looked at the same expression, agree with you that i should be at its maximum, but dont understand the following part:
---------------------------------------------------------------------------------------------------------
"This happens when h = j"

looking at ((h² + j² - i²) / (2hj)), how could you conclude that? I would say h² + j² should be small and i should be as big as possible, but h = j ?
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Also, here is an example triangle (H=30, I = 59, J = 91) with sides (h = 10.00, i = 17.14, j = 20.00) which satisfies the condition that I < 60, but ((h+j-i)) / (h+j)) < 1/2

Thanks again

#3 Help Me ! » Triangle related » 2005-12-10 14:45:59

cevilian
Replies: 7

Hi guys,
I am new to the forum and this is my first post. I need some help with the following problem:

*********************************************************************************
ABC is a triangle, with the length of sides:
AB = h
BC = i
CA = j

If ((h+j-i) / (h+j)) > (1/2), then the angle between the AB and AC is:
1) Less than 60 degrees
(Also: Smaller than the other two angles)
*********************************************************************************
Is the above right? If yes, How do we prove it?

Similarly, for ((h+j-i) / (h+j)) > (1/3, or 1/4 or any other value x such that 0 < x < 1), can we establish an upper and a lower limit on the angle between the AB and AC?

Thanks in advance!

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