[tex]\it \ Fie\ x,\ y,\ z\ m\breve asurile\ celor\ trei\ unghiuri\ ale\ triunghiului\\ \\ \c{S}tim\ c\breve a\ x+y+z=180^o\ \ \ \ \ (1)\\ \\ \{x,\ y,\ z\}\ d.\ p.\ \{5,\ 7,\ 24\} \Rightarrow \dfrac{x}{5}=\dfrac{y}{7}=\dfrac{z}{24}=\dfrac{x+y+z}{5+7+24}\stackrel{(1)}{=}\ \dfrac{180^o}{36}=5^o\ \ \ \ \ (2)\\ \\ \\ (2)\Rightarrow\ \begin{cases}\it x=5\cdot5^o=25^o\\ \\ \it y=7\cdot5^o=35^o\\ \\ \it z=24\cdot5^o=120^o\end{cases}[/tex]
Deci, cel mai mare unghi al triunghiului are măsura 120°.
