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Old   July 13, 2006, 17:30
Default Geometry/Trigonometry Puzzle
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RW
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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, non-parallel, 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.
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Old   July 13, 2006, 19:43
Default Re: Geometry/Trigonometry Puzzle
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Adrin Gharakhani
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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.(s-a).(s-b).(s-c) )

and s = ( a + b + c ) /2

adrin

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Old   July 17, 2006, 15:31
Default 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
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Old   July 17, 2006, 15:36
Default Re: Geometry/Trigonometry Puzzle
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pc
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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?

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Old   July 17, 2006, 16:05
Default Re: Geometry/Trigonometry Puzzle
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Adrin Gharakhani
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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

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Old   July 17, 2006, 17:46
Default Re: Geometry/Trigonometry Puzzle
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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
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Old   July 17, 2006, 17:47
Default Re: Geometry/Trigonometry Puzzle
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Ah, thanks!
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Old   July 30, 2006, 10:14
Default Re:Trigonometry Puzzle
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LaDy_mHiNe08
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i need trigonometry puzzles for my project in mathIV. . . please give me a trigonometry puzzles. . .
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