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July 13, 2006, 17:30 
Geometry/Trigonometry Puzzle

#1 
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Ladies and Gentlemen:
In the course of my CFD work, I've come upon a problem which at first seems nearly trivial, but which, I'm embarassed to say, I haven't solved. Perhaps someone can help.  Consider two line segments of known length.  They are connected together, nonparallel, and the angle they form is known.  Now without disturbing their geometry, consider those two segments as two adjacent, connected chords of a circle. What is the radius of the circle which circumscribes the two segments as valid chords? Thanks in advance. 

July 13, 2006, 19:43 
Re: Geometry/Trigonometry Puzzle

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if one side has length a and the second has length c, and the line connecting the two extremes (to make a triangle) has length b, then the radius R of the circle is
R = a.b.c / (4.D) where D = sqrt( s.(sa).(sb).(sc) ) and s = ( a + b + c ) /2 adrin 

July 17, 2006, 15:31 
Re: Geometry/Trigonometry Puzzle

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Thank you for replying:
In my problem, we don't know the length b. But we do know the angle, phi, that is formed by the vertex of the two line segments. Any ideas? Rich 

July 17, 2006, 15:36 
Re: Geometry/Trigonometry Puzzle

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If you know the end points of the two line segments a and c, then you know the length b, regardless of the angle, do you not?


July 17, 2006, 16:05 
Re: Geometry/Trigonometry Puzzle

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The length c, for known lengths a and b, and the angle C between them is given by the law of cosines:
c^2 = a^2 + b^2  2.a.b.Cos(C) adrin 

July 17, 2006, 17:46 
Re: Geometry/Trigonometry Puzzle

#6 
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We don't know the endpoints. We only know the lengths of the two line segments and the included angle.
Rich 

July 17, 2006, 17:47 
Re: Geometry/Trigonometry Puzzle

#7 
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Ah, thanks!


July 30, 2006, 10:14 
Re:Trigonometry Puzzle

#8 
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i need trigonometry puzzles for my project in mathIV. . . please give me a trigonometry puzzles. . .


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