In $\triangle A B C$, if $a=7, b=8, \tan C=\frac{3 \sqrt{5}}{2}$ and $C$ is an acute angle, then $c=$

In a $\triangle A B C$, if $\frac{a}{\tan A}=\frac{b}{\tan B}=\frac{c}{\tan C}$, then $\cos ^2 A+\cos ^2 B+\cos ^2 C=$

In $\triangle A B C$, if $a=7, b=10$ and $c=11$, then $\frac{R}{r}=$

If $a, b$ and $c$ are the sides of $a \triangle A B C$ and $\left|\begin{array}{lll}b & 1 & a \\ a & 1 & c \\ c & 1 & b\end{array}\right|=0$, then $2(\cos A+\cos B+\cos C)=$