Math Is Fun Forum

Mathsy,
Many thanks indeed for your response. I think, I kinda lost touch with my math fundamentals (makes me 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:
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"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