[tex]\it Fie\ x,\ y,\ z\ m\breve asurile\ celor\ trei \ unghiuri.\\ \\ x+y+z=180^o\ \ \ \ \ (1)\\ \\ \{x,\ \ y,\ \ z\}\ i.\ p.\ \Big\{\dfrac{1}{2},\ \ \dfrac{1}{4},\ \ \dfrac{1}{6}\Big\}\Rightarrow \{x,\ \ y,\ \ z\}\ d.\ p.\ \{2,\ \ 4,\ \ 6\}\Rightarrow \\ \\ \\ \Rightarrow \dfrac{x}{2}=\dfrac{y}{4}=\dfrac{z}{6}=\dfrac{x+y+z}{2+4+6}\ \stackrel{(*)}{=}\ \dfrac{180^o}{12}=15^o \Rightarrow \begin{cases} \it x=2\cdot15^o=30^o\\ \\ \it y=4\cdot15^o=60^o\\ \\ \it z=6\cdot15^o=90^o\end{cases}[/tex]
Triunghiul este dreptunghic, de forma (30, 60, 90)
