Question

unghiurile A,B,C ale unui triunghi au masurile invers proportionale cu 1 pe 5 ,1 pe 6 si 1 pe 7 Aflati masurile unghiurilor

Answer 1

[tex]\{A,B,C\} i.p.\{ \frac{1}{5},\frac{1}{6},\frac{1}{7}\}\Rightarrow \frac{\frac{A}{1}}{\frac{1}{5}}=\frac{\frac{B}{1}}{\frac{1}{6}}=\frac{\frac{C}{1}}{\frac{1}{7}}\Rightarrow \frac{A}{5}=\frac{B}{6}=\frac{C}{6}=K\Rightarrow\\ \Rightarrow A=5k,B=6k, C=7k\\ A+B+C=180\\ 5k+6k+7k=180\\ 18k=180\\ \boxed{k=10}\\ A=5k\Rightarrow \boxed{A=50}\\ B=6k\Rightarrow \boxed{B=60}\\ C=7k \Rightarrow \boxed{C=70}[/tex]