Xét \(\Delta ABH\) vuông tại H:
\(+sinB=\dfrac{AH}{AB}\) (Tỉ số lượng giác).
\(\Rightarrow sin80^o=\dfrac{5}{AB}.\\ \Rightarrow AB=\dfrac{5}{sin80^o}.\\ \Leftrightarrow AB\approx5,08\left(cm\right).\\ \tan B=\dfrac{AH}{BH}\left(TSLG\right).\\ \Rightarrow\tan80^o=\dfrac{5}{BH}.\\ \Rightarrow BH\approx0,89\left(cm\right).\)
Xét \(\Delta AHC\) vuông tại H:
\(+sinC=\dfrac{AH}{AC}\left(TSLG\right).\\ \Rightarrow sin30^o=\dfrac{5}{AC}.\\ \Rightarrow AC=\dfrac{5}{sin30^o}=10\left(cm\right).\\ +\tan C=\dfrac{AH}{HC}\left(TSLG\right).\\ \Rightarrow\tan30^o=\dfrac{5}{HC}.\\ \Rightarrow HC=5\sqrt{3}\left(cm\right).\)
\(BC=BH+HC\approx0,89+5\sqrt{3}\approx9,55\left(cm\right).\)
