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 $\ell(A C)=$

In a $$\triangle A B C$$ if $$2 \cos C=\sin B \cdot \operatorname{cosec} A$$, then

In a triangle $$A B C$$ with usual notations, if $$\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}$$, then area of triangle $$A B C$$ with $$a=\sqrt{6}$$ is

In a triangle $$A B C$$, if $$\frac{\sin A-\sin C}{\cos C-\cos A}=\cot B$$, then $$A, B, C$$, are in