[tex]\displaystyle \\
In~ \Delta ABC~avem: \\
\ \textless \ A,~\ \textless \ B,~\ \textless \ C~\texttt{sunt direct proportionale cu 6; 9 si 15. } \\ \\
\frac{A}{6}= \frac{B}{9} = \frac{C}{15} =k \\ \\
A=6k \\
B = 9k \\
C=15k \\
\ \textless \ A + \ \textless \ B+\ \textless \ C = 180^o \\
6k+9k+15k = 180^o \\
30k = 180 \\ \\
k = \frac{180}{30} = \boxed{6} \\ \\
A=6k = 6 \times 6 = \boxed{36^o }\\
B = 9k = 9 \times 6 = \boxed{54^o } \\
C=15k = 15 \times 6 = \boxed{90^o} \\ \\
\texttt{Rezulta ca triunghiul este dreptunghic.}
[/tex]