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#1 2015-09-05 19:52:41

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,762

The Sine Rule

In any triangle ABC,

where R is the radius of the circumcircle.

dExW77C.gif


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


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

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#2 2016-04-25 18:53:52

thickhead
Member
Registered: 2016-04-16
Posts: 1,022

Re: The Sine Rule

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


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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