Đáp án:
Áp dụng tc đường phân giác trong tg ta có:
$\begin{array}{l}
BC = BD + CD = 75 + 110 = 185\\
\Rightarrow \dfrac{{AB}}{{BD}} = \dfrac{{AC}}{{CD}}\\
\Rightarrow \dfrac{{AB}}{{75}} = \dfrac{{AC}}{{110}}\\
\Rightarrow \dfrac{{AB}}{{15}} = \dfrac{{AC}}{{22}}\\
Theo\,Pytago:\\
A{B^2} + A{C^2} = B{C^2}\\
\Rightarrow {\left( {\dfrac{{15}}{{22}}AC} \right)^2} + A{C^2} = {185^2}\\
\Rightarrow \dfrac{{709}}{{484}}A{C^2} = {185^2}\\
\Rightarrow AC = 152,85\left( {cm} \right)\\
\Rightarrow AB = \dfrac{{15}}{{22}}AC = 104,22\left( {cm} \right)\\
A{C^2} = CH.BC\\
\Rightarrow CH = \dfrac{{A{C^2}}}{{BC}} = 126,29\left( {cm} \right)\\
\Rightarrow DH = CH - CD = 16,29\left( {cm} \right)
\end{array}$
