If angles A,B,C of a triangle ABC form an increasing AP,then sin B is ????

Asked by Saloni | 29th Jun, 2014, 11:52: AM

Expert Answer:

 Sum space of space all space the space angles space of space the space triangle space is 180 to the power of degree.  text Therefore ,  end text A plus B plus C equals 180 to the power of degree.  text Also   end text A comma space B comma space C text   are   in   AP end text.  L e t space d space b e space t h e space c o m m o n space d i f f e r e n c e space o f space t h e space A P.  T h e r e f o r e space B space a n d space C space c a n space b e space r e p r e s e n t e d space a s comma  B equals A plus d space a n d space C equals A plus 2 d.  A plus B plus C equals 180 to the power of degree A plus open parentheses A plus d close parentheses plus open parentheses A plus 2 d close parentheses equals 180 to the power of degree 3 A plus 3 d equals 180 to the power of degree A plus d equals 60 to the power of degree B equals 60 to the power of degree  sin B equals sin 60 to the power of degree equals fraction numerator square root of 3 over denominator 2 end fraction

Answered by Vijaykumar Wani | 30th Jun, 2014, 10:11: AM