\[\begin{array}{l}
AH = 4cm;\,\,CH = 9cm\\
Ap\,\,\,dung\,\,he\,\,thuc\,\,luong\,\,trong\,\,tam\,\,giac\,\,vuong\,\,\,ta\,\,co:\\
A{H^2} = BH.HC \Rightarrow BH = \frac{{A{H^2}}}{{HC}} = \frac{{{4^2}}}{9} = \frac{{16}}{9}\,\,cm.\\
\Rightarrow BC = BH + CH = 9 + \frac{{16}}{9} = \frac{{97}}{9}\,\,cm.\\
A{B^2} = BH.HC = \frac{{16}}{9}.9 = 16 \Rightarrow AB = 4cm.\\
\Rightarrow AC = \sqrt {B{C^2} - A{B^2}} = \sqrt {{{\left( {\frac{{97}}{9}} \right)}^2} - 16} = \frac{{\sqrt {8113} }}{9}\\
b)\,\,\,\sin B = \frac{{AC}}{{BC}} = \frac{{\sqrt {8113} }}{9}.\frac{9}{{97}} = \frac{{\sqrt {8113} }}{{97}}.\\
\tan C = \frac{{AB}}{{AC}} = \frac{4}{{\frac{{\sqrt {8113} }}{9}}} = \frac{{36}}{{\sqrt {8113} }}.\\
\Rightarrow C = {21^0}47.
\end{array}\]
