Question

Aflati masurile unghiurilor triunghiului ABC stiind ca m(A)=6/11m(B)=6/19m(C)

Answer 1

 

$\displaystyle\\\text{Propun sa simplificam notatia unghiurilor} \\\text{scriind A, B, C in loc de m(A), m(B), m(C)}\\\\\text{Rezolvare:}\\\\A=\frac{6}{11}B=\frac{6}{19}C\\\\B=\frac{11}{6}A\\\\C=\frac{19}{6}A\\\\A+B+C=180^o\\\\A+\frac{11}{6}A+\frac{19}{6}A=180^o\\\\A\left(1+\frac{11}{6}+\frac{19}{6}\right)=180^o\\\\A\times\frac{6+11+19}{6}=180^o\\\\\frac{36}{6}A=180^o$

$\displaystyle\\6A=180^o\\\\A=\frac{180^o}{6}\\\\\boxed{A=30^o}\\\\B=\frac{11}{6}A=\frac{11}{6}\times30=11\times5=55^o\\\\\boxed{B=55^o}\\\\C=\frac{19}{6}A=\frac{19}{6}\times30=19\times5=95^o\\\\\boxed{C=95^o}\\\\\text{Verificare:}\\\\A+B+C=30^o+55^o+95^o=180^o$