\(\Delta AHB\) vuông tại \(H\)
\(\Rightarrow sin45^0=\dfrac{AH}{AB}=\dfrac{9}{AB}\)
\(\Rightarrow AB=\dfrac{9}{sin45^0}=9\sqrt{2}\left(cm\right)\)
\(\Delta AHB\) vuông tại \(H\)
\(\Rightarrow cos45^0=\dfrac{HB}{AB}=\dfrac{HB}{9\sqrt{2}}\)
\(\Rightarrow HB=9\sqrt{2}.cos45^0=9\left(cm\right)\)
\(\Delta AHC\) vuông tại \(H\)
\(\Rightarrow sinC=\dfrac{AH}{AC}=\dfrac{9}{6\sqrt{3}}=\dfrac{\sqrt{3}}{2}\) \(\Rightarrow\widehat{C}=60^0\)
\(\Rightarrow c\text{os}60^0=\dfrac{HC}{AC}=\dfrac{HC}{6\sqrt{3}}\)\(\Rightarrow HC=6\sqrt{4}.c\text{os}60^0=6\left(cm\right)\)
\(\Leftrightarrow BC=BH+HC=9+6=15\left(cm\right)\)