Tam giác AHB vuông ( gt ), ta có:
\(AH^2+BH^2=AB^2\left(Pytago\right)\)
\(\Rightarrow BH^2=AB^2-AH^2\)
\(\Rightarrow BH=\sqrt{13^2-5^2}=12\left(cm\right)\)
Tam giác AHC vuông ( gt ), ta có:
\(AH^2+CH^2=AC^2\)
\(\Rightarrow CH^2=AC^2-AH^2\)
\(\Rightarrow CH=\sqrt{9^2-5^2}=2\sqrt{14}\)