\(BC=\sqrt{AB^2+AC^2}=2\sqrt{89}\left(cm\right)\left(pytago\right)\\ \sin\widehat{B}=\cos\widehat{C}=\dfrac{AC}{BC}=\dfrac{16}{2\sqrt{89}}=\dfrac{8\sqrt{89}}{89}\\ \cos\widehat{B}=\sin\widehat{C}=\dfrac{AB}{BC}=\dfrac{10}{2\sqrt{89}}=\dfrac{5\sqrt{89}}{89}\\ \tan\widehat{B}=\cot\widehat{C}=\dfrac{AC}{AB}=\dfrac{16}{10}=1,6\\ \cot\widehat{B}=\tan\widehat{C}=\dfrac{AB}{AC}=\dfrac{10}{16}=0,625\)
Xét tam giác ABC vuông tại A:
\(BC^2=AB^2+AC^2\left(pytago\right)\)
\(\Rightarrow BC=\sqrt{AB^2+AC^2}=\sqrt{10^2+16^2}=2\sqrt{89}\left(cm\right)\)
Áp dụng tslg trong tam giác ABC vuông tại A:
\(\left\{{}\begin{matrix}sinB=\dfrac{AC}{BC}=\dfrac{16}{2\sqrt{89}}=\dfrac{8\sqrt{89}}{89}\\cosB=\dfrac{AB}{BC}=\dfrac{10}{2\sqrt{89}}=\dfrac{5\sqrt{89}}{89}\\tanB=\dfrac{AC}{AB}=\dfrac{16}{10}=\dfrac{8}{5}\\cotB=\dfrac{AB}{AC}=\dfrac{10}{16}=\dfrac{5}{8}\end{matrix}\right.\)
\(\left\{{}\begin{matrix}sinC=\dfrac{AB}{BC}=\dfrac{10}{2\sqrt{89}}=\dfrac{5\sqrt{89}}{89}\\cosC=\dfrac{AC}{BC}=\dfrac{16}{2\sqrt{89}}=\dfrac{8\sqrt{89}}{89}\\tanC=\dfrac{AB}{AC}=\dfrac{10}{16}=\dfrac{5}{8}\\cotC=\dfrac{AC}{AB}=\dfrac{16}{10}=\dfrac{8}{5}\end{matrix}\right.\)