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Question

In a triangle ABC, if A,B,C are in A.P and b:c=3:2, then A

A
450
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B
600
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C
750
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D
300
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Solution

The correct option is C 750
A,B,C are in A.P.
A+C=2B
πB=2B (A+B+C=π)
3B=π or B=π3=600
Given b:c=3:2
sinBsinC=3:2
sin600sinC=3:2
32sinC=32
2sinC=2
sinC=22×22 (by rationalizing the numerator)
On simplifying we get
sinC=12
C=450
A=1800(B+C)=1800(600+450)=750 (on simplification)
Hence,A=750

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