\(BC=\sqrt{AB^2+AC^2}=5\left(cm\right)\left(pytago\right)\)
Áp dụng HTL:
\(\left\{{}\begin{matrix}AB^2=BH\cdot BC\\AC^2=CH\cdot BC\\AH^2=HB\cdot CH\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}BH=\dfrac{AB^2}{BC}=1,8\left(cm\right)\\CH=\dfrac{AC^2}{BC}=3,2\left(cm\right)\\AH=\sqrt{1,8\cdot3,2}=2,4\left(cm\right)\end{matrix}\right.\)