TRIGONOMETRY : Properties of Triangles

Properties of Triangles

Consider a triangle ABC.it has three angles A,B and C.The sides opposite to the angles A,B,C are denoted by the corresponding small letters a,b,c respectively.

Thus a=BC,b=CA,c=AB in the fig. shown below.

Sine Formula : 

 a/sina  = b/sinB=c/sinc=2R  Where R,is a Radius of Circle circum circle of the triangle.

Napier's Formulae :

 

Cosine Formulae:

1. a²=b²+c² -2bc cosA
2. b²=c²+a² -2ca cosB
3. c²=a²+b² -2ab cosC

Projection Formulae : 

1. a =bcosC+ccosB
2. b=ccosA+acosC
3. c=acosB+bcosA

 Half Angle Formulae :

 

Area Formulae: