[tex]\it tgA=\dfrac{BC}{AC} =\dfrac{24}{7}\Rightarrow \dfrac{BC}{24}=\dfrac{AC}{7}=k\Rightarrow \begin{cases}\it BC=24k\\ \\ \it AC=7k\end{cases}\ \ \ \ \ (1)\\ \\ \\ ABC\ dreptunghic,\ m(\hat C)=90^o \stackrel{T.Pitagora}{\Longrightarrow}\ AC^2+BC^2=AB^2 \ \ \ \ (2)\\ \\ (1),(2) \Rightarrow (7k)^2+(24k)^2=25^2 \Rightarrow 49k^2+576k^2=625 \Rightarrow 625k^2=625\Rightarrow\\ \\ \Rightarrow k^2=1\Rightarrow k=1\ \ \ \ \ (3)[/tex]
[tex]\it (1),(3)\Rightarrow BC=24cm,\ \ AC = 7cm[/tex]
