Răspuns:
90°, 54°, 36°; dreptunghic
Explicație pas cu pas:
fie ΔABC
[tex]\hat A + \hat B + \hat C = 180 \degree[/tex]
invers proporționale:
[tex]\hat A \cdot 0,2 = \hat B \cdot 0,(3) = \hat C \cdot 0,5[/tex]
[tex]\hat A \cdot \frac{2}{10} = \hat B \cdot \frac{3}{9} = \hat C \cdot \frac{5}{10} \iff \hat A \cdot \frac{1}{5} = \hat B \cdot \frac{1}{3} = \hat C \cdot \frac{1}{2} \\\frac{\hat A}{5} = \frac{\hat B}{3} = \frac{\hat C}{2} = \frac{\hat A + \hat B + \hat C}{5 + 3 + 2} = \frac{180\degree}{10} = 18 \degree[/tex]
[tex]\frac{\hat A}{5} = 18 \degree \implies \bf \hat A = 90 \degree\\ \frac{\hat B}{3} = 18 \degree \implies \bf \hat B = 54 \degree\\ \frac{\hat C}{2} = 18 \degree \implies \bf \hat C = 36 \degree[/tex]
∢A = 90° => ΔABC este dreptunghic
