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  3. CEE Kerala Engineering

CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2004

  • question_answer
    The perimeter of a triangle ABC is 6 times the arithmetic mean of the sine ratios of its angles. If\[a=1,\]then A is equal to:

    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 \[a=1\] \[\therefore \]  \[\sin A=\frac{1}{2}=\sin \frac{\pi }{6}\] \[\Rightarrow \]               \[A=\frac{\pi }{6}\]


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