1: \(BC=\sqrt{2+2}=2\left(cm\right)\)
\(AH=\dfrac{AB\cdot AC}{BC}=1\left(cm\right)\)
\(BH=\dfrac{AB^2}{BC}=1\left(cm\right)\)
CH=BC-BH=1cm
2: \(BC=\sqrt{6^2+11^2}=\sqrt{157}\left(cm\right)\)
\(AH=\dfrac{AB\cdot AC}{BC}=\dfrac{66\sqrt{157}}{157}\left(cm\right)\)
\(BH=\dfrac{AB^2}{BC}=\dfrac{121\sqrt{157}}{157}\left(cm\right)\)
\(CH=\dfrac{AC^2}{BC}=\dfrac{36\sqrt{157}}{157}\left(cm\right)\)