Math Is Fun Forum

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

The Sine Rule

In any triangle ABC,

where R is the radius of the circumcircle.

If you are not yet familiar with the construction of a circumcircle and the angle properties of a circle, you are advised to look these up first.

The circumcircle

http://www.mathisfunforum.com/viewtopic … 40#p367140

Angle properties of a circle.

http://www.mathisfunforum.com/viewtopic.php?id=17799
Posts 6 and 7

Proof

angle AOF = half angle AOB = ACB (using the angle props)

Therefore

The rest follows by a  similar argument.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: The Sine Rule

Last edited by thickhead (2016-04-25 18:58:06)

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
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{Gods rejoice at those places where ladies are respected.}