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# Law of Sines?

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A friend of mine made this picture to illustrate the law of sines: http://img27.photobucket.com/albums/v81/Krakkles/law_of_sines.jpg I kinda see a pattern, but not completely...and I don't know how this knowledge would be useful. [edited by - Krak on March 24, 2004 10:25:47 AM]

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http://img27.photobucket.com/albums/v81/Krakkles/law_of_sines.jpg

In case anyone has difficulty finding it.

The "law of sines" allows you to find any length given 2 angles and a length. I''m sure someone else, who has used it in the past few years can give a more satifactory explanation.

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x/(sin X) = y/(sin Y) = z/(sin Z) where x, y and z are the lengths of sides and X, Y and Z are the angles opposite them.

The complement to the Law of Sines (we called it Sine Rule in high school) is the Cosine Rule:
x2 = y2 * z2 - 2yz*(cos X)

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quote:
Original post by Oluseyi
x2 = y2 * z2 - 2yz*(cos X)

Should be
x2 = y2 + z2 - 2yz*(cos X)

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And then there were vectors...

BTW, my text book uses:

a b c
--- = --- = ---
sinA sinB SinC

But x,y,z is much better. Now I won''t confuse side "a" with angle "A".

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The "Law Of Sines" or as us Britishers tend to call it the "Sine Rule" Allows you to find the length of the side of any triangle given two angles and a side, or two sides and an angle.

Very useful for triangles of forces when dealing with forces in mechanical situations especialy when put alongside the "cosine rule"
a^2 = b2 + c2 - 2bccosA

Which gives you the length of a side given two sides and an angle etc...

EDIT: Typeo
---------

Does it matter? Even if it does matter, does it matter that it matters?

[edited by - SonOfNed on March 24, 2004 2:01:52 PM]

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quote:
Original post by higherspeed
The "law of sines" allows you to find any length given 2 angles and a length. I'm sure someone else, who has used it in the past few years can give a more satifactory explanation.

Just to add to this, the Law of Sines can also work with two sides and an angle, as long as the angle IS NOT contained between the two sides. In that case we would go to the Law of Cosines.

[edited by - porthios on March 24, 2004 2:08:11 PM]

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We would use the cosine law for any combination of 2 sides and an angle. Well that would be the quickest way. Not that it really matters either way.

[edited by - higherspeed on March 24, 2004 5:06:01 PM]

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A slightly stronger version of the law of sines is this:
a/sin(A) = b/sin(B) = c/sin(C) = 2R,
where R is the radius of the circumference that contains A, B and C.

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