MHT CET · Maths · Properties of Triangles
With usual notations, the perimeter of a triangle ABC is 6 times the arithmetic mean of sine of its angles. If \(a=1\), then \(\angle \mathrm{A}=\)
- A \(\frac{\pi}{6}\)
- B \(\frac{\pi}{3}\)
- C \(\frac{\pi}{2}\)
- D \(\frac{2 \pi}{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{6}\)
Step-by-step Solution
Detailed explanation
\( a+b+c = 6 \left( \frac{\sin A + \sin B + \sin C}{3} \right) \) \( 2R\sin A + 2R\sin B + 2R\sin C = 2(\sin A + \sin B + \sin C) \)
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