TS EAMCET · Maths · Properties of Triangles
The perimeter of a \(\triangle A B C\) is 6 times the arithmetic mean of the sine of its angles. If its side \(B C\) is of unit length, then \(\angle A=\)
- A \(\frac{\pi}{6}\)
- B \(\frac{\pi}{3}\)
- C \(\frac{\pi}{2}\)
- D \(\pi\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{6}\)
Step-by-step Solution
Detailed explanation
It is given that length of side \(B C=1\) unit, then according to the given information \(a+b+c=6 \frac{\sin A+\sin B+\sin C}{3}\) \(\Rightarrow a+b+c=2(\sin A+\sin B+\sin C)\) \(\Rightarrow \quad 2 R(\sin A+\sin B+\sin C)=2\) \((\sin A+\sin B+\sin C) \quad(\) from sine law…
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