sines law proof

Let ABC a triangle. Let T a point in the circumcircleMathworldPlanetmath such that BT is a diameterMathworldPlanetmathPlanetmath.

So A=CAB is equal to CTB (they subtend the same arc). Since CBT is a right triangle, from the definition of sine we get


On the other hand CAB=CTB implies their sines are the same and so


and therefore


Drawing diameters passing by C and A will let us prove in a similarMathworldPlanetmath way the relations


and we conclude that



Title sines law proofPlanetmathPlanetmath
Canonical name SinesLawProof
Date of creation 2013-03-22 11:57:36
Last modified on 2013-03-22 11:57:36
Owner drini (3)
Last modified by drini (3)
Numerical id 9
Author drini (3)
Entry type Proof
Classification msc 51-00
Related topic CosinesLaw
Related topic Triangle
Related topic SinesLaw