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Dave Lindell
Posts: 14
Location: Hacienda Heights, USA
Joined: 10/20/2008
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Welcome |
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Oh, oh. Now you've got us right where you want us: at your fingertips!
I'm sure Ben and I would be glad to answer for our mistakes on this forum, but I don't think Ben has made any.
It may be difficult to answer with equations, but I can always type an answer and convert it to a ".pdf" if need be.
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Tuesday, October 28, 2008 at 7:00:59 PM |
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Pierce
Posts: 3
Joined: 5/7/2009
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Re: Prob 184 |
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Dave,
I found your solution to Problem 184 to be a bit lengthy and complicated ... wouldn't it be easier to first solve for Angle 'C' using the formula for the length of a bisector, and then once you have Angle 'C', all you need to do is plug it into the Law of Cosines to get length AB.
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Thursday, May 07, 2009 at 3:29:12 PM |
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Dave Lindell
Posts: 14
Location: Hacienda Heights, USA
Joined: 10/20/2008
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Re: Welcome |
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O.K., I'll bite. What is the "formula for the length of a bisector"? It's given in this problem.
I'm always willing to learn something new, though. I've overlooked obvious solutions before!
This problem is unique because the angle "C" is NOT given or able to be solved with the information given, at least not directly. Another thing, it doesn't matter what it is in this problem.
Another solution brought to my attention by Ross Whislter is to fold the triangle along the line CQ and then...I'll let you take it from there.
Thanks for your interest.
Dave Lindell
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Sunday, May 10, 2009 at 6:17:36 PM |
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Pierce
Posts: 3
Joined: 5/7/2009
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Re: Welcome |
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CQ = ([2cos(C/2)][AC][BC])/(AC+BC) so solving for angle C you get 2*cos-1 {[CQ(AC+BC)]/2(AC)(BC)}.
Once you have angle C you are able to use the law of cosines to derive the length AB.
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Monday, May 11, 2009 at 11:05:46 AM |
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Dave Lindell
Posts: 14
Location: Hacienda Heights, USA
Joined: 10/20/2008
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Re: Welcome |
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I'm impressed! That's a nifty formula.
Your first statement is correct, but it reduces to CQ(AC+BC)/2 AC BC = cos(C/2)
Where did you find this formula?
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Wednesday, May 13, 2009 at 9:14:15 PM |
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Pierce
Posts: 3
Joined: 5/7/2009
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Re: Welcome |
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Thanks!
Max A. Sobel and Norbert Lerner. 1991. Precalculus Mathematics. Prentice Hall. 4th ed.
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Tuesday, May 19, 2009 at 9:49:52 AM |
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