Explicație pas cu pas:
[tex]T_{1}: \frac{ \alpha_{1} }{2} = \frac{ \beta_{1} }{1} = \frac{ \gamma_{1} }{6} = \frac{ \alpha_{1} + \beta_{1} + \gamma_{1} }{2 + 1 + 6} = \frac{180}{9} = 20 \\ [/tex]
[tex] \alpha_{1} = 2 \times 20 = 40 \\ \beta_{1} = 1 \times 20 = 20 \\ \gamma_{1} = 6 \times 20 = 120[/tex]
→ triunghiul nu este dreptunghic
[tex]T_{2}: \frac{ \alpha_{2} }{5} = \frac{ \beta_{2} }{7} = \frac{ \gamma_{2} }{6} = \frac{ \alpha_{2} + \beta_{2} + \gamma_{2} }{5 + 7 + 6} = \frac{180}{18} = 10 \\ [/tex]
[tex]\alpha_{2} = 5 \times 10 = 50 \\ \beta_{2} = 7 \times 10 = 70 \\ \gamma_{2} = 6 \times 10 = 60[/tex]
→ triunghiul nu este dreptunghic
[tex]T_{3}: \frac{ \alpha_{3} }{18} = \frac{ \beta_{3} }{7} = \frac{ \gamma_{3} }{11} = \frac{ \alpha_{3} + \beta_{3} + \gamma_{3} }{18 + 7 + 11} = \frac{180}{36} = 5 \\[/tex]
[tex]\alpha_{3} = 18 \times 5 = 90 \\ \beta_{3} = 7 \times 5 = 35 \\ \gamma_{3} = 11 \times 5 = 55[/tex]
→ triunghiul este dreptunghic
