Q. 175.0( 4 Votes )

If angles A, B, C of a ΔABC form an increasing AP, then sin B =
A. 1/2

B. √3/2

C. 1

D. 1/√2

Answer :

Let suppose A, B and C are the angles of a triangle ABC,


17.bmp


In ∆ABC,


A = (a – d)


B = a


C = a + d


Now, form an increasing A.P


As we know Sum of all the angle of a triangle is 180°,


Therefore,


A + B + C = 180°


(a – d) + a + (a + d) = 180°


3a = 180°


a = 180/3 = 60°


From the table,


sin B = sin A = sin 60°


= √3/2

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