Notam AC=b si BC=a
sin B=b/a
[tex] \frac{b}{a}= \frac{3}{5} \\ \\ \frac{b}{3}= \frac{a}{5}=k \\ \\ b=3k; a=5k [/tex].
Din teorema lui Pitagora avem:
[tex]AB^2+AC^2=BC^2 \\ \\ 6^2+b^2=c^2
\\ \\ 36+(3k)^2=(5k)^2 \\ \\ 36+9k^2=25k^2 \\ \\ 36=16k^2 \\ \\ k^2= \frac{36}{16} \\ k= \sqrt{\frac{36}{16} } =\frac{6}{4}=\frac{3}{2} \\ \\ b=3k=3*\frac{3}{2}=4,5cm} \\ \\ a=5k=5*\frac{3}{2}=\frac{15}{2}=7,5cm [/tex]
