Contents

Sine Rule

Solution of Triangle (Sine)

Cosine Rule

Solution of Triangle (Cosine)

Quiz 

Trigonometry Main Page

Sine Rule

Case 1 (If A is an acute angle)

Consider angle A

Now      ÐBAC = ÐBPC (Ðs in same segment)

Case 2 (If A is an obtuse angle)

Now  ÐBAC + ÐBPC = 180° (opp.  of cyclic quad.) 

                    ÐBAC = 180° - ÐBPC 

               sin ÐBAC = sin (180° - ÐBPC) 

                            = sin ÐBPC

               sin ÐBPC = BC/BP

                            = a/2R

                    sin A = a/2R 

                        2R = a/sin A

 

Similarly, by considering ÐB and ÐC, it can be proved that

 

where b = AC, the side opposite angle B, and c = AB, the side opposite angle c.

 

Hence,

 

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