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In triangle ABC with the usual notations prove that a/sin A = b/sin B = c/sin C

In triangle ABC with the usual notations prove that a/sin A = b/sin B = c/sin C
 

Grade:11

1 Answers

Arun
25750 Points
6 years ago
Dear student
 
I have proved it using vectors.
 

In Triangle ABC, The area of triangle ABC = 1/2*|ABxAC| = 1/2*|ABxBC| = 1/2*|BCxAC|

 

= 1/2*|AB||AC| sin A = = 1/2*|CB||AB| sin B= 1/2*|BC||AC| sin C

 b.c.sin(A)/2 = a.c.sin(B)/2 = a.b.sin(C)/2 b.c.sin(A) =a.c.sin(B) = a.b.sin(C)dividing through by a.b.c, we get a/sin A = b/sin B = c/sin C
 
 
 
 
 

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