Question

In a $\Delta ABC,a=1$ and the perimeter is six times the $AM$ of the sines of the angles. The measure of $\angle A$ is

• A. $\frac{\pi }{3}$
• B. $\frac{\pi }{2}$
• C. $\frac{\pi }{6}$
• D. $\frac{\pi }{4}$

Answer 1

The correct option is C $\frac{\pi }{6}$

$1+b+c=\frac{\sin A+\sin B+\sin C}{3}$

$=2(\frac{1}{2R}+\frac{b}{2R}+\frac{c}{2R})=\frac{1}{R}(1+b+c)$

For $R=1$

$\frac{1}{\sin A}=2R=2$

$\Rightarrow \angle A=\frac{\pi }{6}$