Hatrack River Forum: For Those Who Enjoy Math.

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Posted by Pythagoras (Member # 7024) on :

Let A,B, and C be the vertices of any triangle with side lengths a,b, and c

a) show that bc cosA + ca cosB + ab cos c= (a^2+b^2+c^3)/2

b) describe the special case that occurs for the right triangle.

Show all your work. I will inform you if you are correct or incorrect. Enjoy!

[ November 11, 2004, 09:18 PM: Message edited by: Pythagoras ]

Posted by fugu13 (Member # 2859) on :

*rolls eyes*

Posted by Tatiana (Member # 6776) on :

I think you have typos in your post. Please edit for accuracy?

Posted by Pythagoras (Member # 7024) on :

Certainly.

Posted by Phanto (Member # 5897) on :

: D [Big Grin]

SA DS DS MXC

!!!

MAS

[Smile]

Posted by Pythagoras (Member # 7024) on :

Since I have no idea what you are trying to articulate, I will simply tell you that no, that is not the answer.

Posted by King of Men (Member # 6684) on :

I shall prove this in several ways.

1) By inspection. We can easily see that.

2) By private communication. See reference [1].

3) By generalisation. The proposition is trivally true for the case of A = 90, B=C=45, a = sqrt(2), b=c=1. Therefore, waving our hands a little, it seems reasonable to assume it true for the general case.

[1] Leon Lederman, private conversation. I did actually meet Lederman (Nobel Prize winner 1988, if you didn't know) the other day. Very funny guy.

Posted by Phanto (Member # 5897) on :

Actually, I'm right.

Boo,yeah!

Robot, robot, robot -- ya teba lublu!

Posted by rivka (Member # 4859) on :

Mr. Pythagoras, sir . . . do your own darn homework. [Razz]

Posted by King of Men (Member # 6684) on :

Incidentally, just from symmetry, I suspect the exponent of the final 'c' should be 2, not 3. And perhaps you swapped two numbers here, so the divisor on the right-hand side should be 3?

Posted by MEC (Member # 2968) on :

quote:
bc cosA + ca cosB + ab cos c= (a^2+b^2+c^3)/2

do you mean b*c*cosA + c*a*cosB + a*b*cosC ?

Posted by Dragon (Member # 3670) on :

42

Posted by mr_porteiro_head (Member # 4644) on :

wibble

Posted by Jar Head (Member # 7018) on :

Hey can I just send you my log book? Looks like you could make it clear how I can cover 800 miles at 55 in 11 hours.
[No No]