Maths-
General
Easy

Question

The perimeter of a Δ ABC is 6 times the A.M of the sines of its angles if the side "a" is 1, then the angle A is

  1. straight pi over 6
  2. straight pi over 3
  3. straight pi over 2
  4. straight pi

hintHint:

if a triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c . In this question, we have to find value of if the side "a" is 1, then the angle A = ?.

The correct answer is: straight pi over 6


    T h e space a n g l e s space o f space t h e space t r i a n g l e space A B C space a r e space d e n o t e d space b y space A comma space B comma space C space a n d space t h e space c o r r e s p o n d i n g space o p p o s i t e space s i d e s space b y space a comma space b comma space c.
s o space W e space k n o w space t h a t comma space
fraction numerator a over denominator sin space A end fraction space equals space fraction numerator b over denominator sin space B end fraction space equals space fraction numerator c over denominator sin space C end fraction space equals 2 R
    If a triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c
    A.M of the sines of its angles = fraction numerator sin A space plus space sin B space plus space sin c over denominator 3 end fraction
    According to question, The perimeter of a Δ ABC is 6 times the A.M of the sines of its angles.
    so, a + b + c = 6 x fraction numerator sin A space plus space sin B space plus space sin c over denominator 3 end fraction
         a + b + c = 2 x ( sin A space plus space sin B space plus space sin c )               { fraction numerator a over denominator sin space A end fraction space equals space fraction numerator b over denominator sin space B end fraction space equals space fraction numerator c over denominator sin space C end fraction space equals 2 R }
        space a space plus space b space plus space c space equals space space left parenthesis a over R space plus space b over R space plus c over R right parenthesis space space
s o comma space R equals 1
w e space k n o w space fraction numerator a over denominator 2 R end fraction space equals space sin A space left curly bracket space G i v e n space t h a t space a equals 1 space right curly bracket
1 half space equals space sin A space s o comma space A equals space straight pi over 6

    The angles of the triangle ABC are denoted by A, B, C and the corresponding opposite sides by a, b, c.

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