1) Đặt \(AB=8k;BC=17k\left(k\in Q\right)\)
\(sinC=\dfrac{AB}{BC}=\dfrac{8k}{17k}=\dfrac{8}{17}\)
\(AC^2+AB^2=BC^2\left(Pitago\right)\)
\(\Leftrightarrow AC^2=BC^2-AB^2=289k^2-64k^2=225k^2\)
\(\Leftrightarrow AC^2=15k\)
\(cosC=\dfrac{AC}{BC}=\dfrac{15k}{17k}=\dfrac{15}{17}\)
\(tanC=\dfrac{AB}{AC}=\dfrac{7k}{15k}=\dfrac{7}{15}\)
\(cotC=\dfrac{1}{tanC}=\dfrac{15}{7}\)
2) Đặt \(AB=5k;AC=12k\left(k\in Q\right)\)
\(cotB=\dfrac{AB}{AC}=\dfrac{5k}{12k}=\dfrac{5}{12}\)
\(BC^2=AB^2+AC^2\left(Pitago\right)\)
\(\Leftrightarrow BC^2=25k^2+144k^2=169k^2\)
\(\Leftrightarrow BC=13k\)
\(sinB=\dfrac{AC}{BC}=\dfrac{12k}{13k}=\dfrac{12}{13}\)
\(cosB=\dfrac{AB}{BC}=\dfrac{5k}{13k}=\dfrac{5}{13}\)
\(tanB=\dfrac{1}{cotB}=\dfrac{12}{5}\)
