A) \[\frac{\pi }{6}\]
B) \[\frac{\pi }{3}\]
C) \[\frac{\pi }{2}\]
D) \[\frac{2\pi }{3}\]
E) \[\frac{3\pi }{4}\]
Correct Answer: A
Solution :
Let a, b, c be the sides of triangle, then \[a+b+c=\frac{6}{3}(sin\text{ }A+sin\text{ }B+sin\text{ }C)\] \[\Rightarrow \] \[a+b+c=2(sin\text{ }A+sin\text{ }B+sin\text{ }C)\] \[\Rightarrow \] \[\frac{a}{2}=\sin A\] But \[a=1\] \[\therefore \] \[\sin A=\frac{1}{2}=\sin \frac{\pi }{6}\] \[\Rightarrow \] \[A=\frac{\pi }{6}\]You need to login to perform this action.
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