Difference between revisions of "Law of Sines"
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Revision as of 15:48, 7 October 2007
Given a triangle with sides of length a, b and c, opposite angles of measure A, B and C, respectively, and a circumcircle with radius R, .
Contents
Proof
Method 1
In the diagram below, circle circumscribes triangle . is perpendicular to . Since , and . But making . Therefore, we can use simple trig in right triangle to find that
The same holds for b and c thus establishing the identity.
This picture could be replaced by an asymptote drawing. It would be appreciated if you do this.
Method 2
This method only works to prove the regular (and not extended) Law of Sines.
The formula for the area of a triangle is:
Since it doesn't matter which sides are chosen as , , and , the following equality holds:
Multiplying the equation by yeilds: