With usual notations, perimeter of a triangle $$A B C$$ is 6 times the arithmetic mean of sine of its angles. If $$\mathrm{a}=1$$, then measure of angle $$\mathrm{A}=$$

With usual notations if the angles of a triangle are in the ratio 1 : 2 : 3, then their corresponding sides are in the ratio.

With usual notations, if the angles $A, B, C$ of a $\triangle A B C$ are in $A P$ and $b: c=\sqrt{3}: \sqrt{2}$

The area of the $\triangle A B C$ is $10 \sqrt{3} \mathrm{~cm}^2$, angle $B$ is $60^{\circ}$ and its perimeter is 20 cm , then $\ell(A C)=$