Giải thích các bước giải:
$\begin{array}{l}
a)apdung\,he\,thuc\,luong\,trong\,tam\,giac\,vuong\,\\
+ co:A{H^2} = CH.BH = 2.6 = 12\\
\Rightarrow AH = \sqrt {12} \left( {cm} \right)\\
+ \,A{B^2} = BH.BC = 2.\left( {2 + 6} \right) = 16\\
\Rightarrow AB = 4\left( {cm} \right)\\
b)\\
\frac{{\cot B}}{{\cot C}} = \frac{{AB}}{{AC}}:\frac{{AC}}{{AB}} = \frac{{A{B^2}}}{{A{C^2}}} = \frac{{A{B^2}}}{{B{C^2} - A{B^2}}} = \frac{{16}}{{{8^2} - {4^2}}} = \frac{1}{3}
\end{array}$