[tex]\it \widehat{CAB}=\widehat{DCA}\ (alterne\ interne)\ \ \ \ \ (1)\\ \\ \widehat{BCA}=\widehat{CDA}\ -\ obtuze\ \ \ \ \ \ (2)\\ \\ (1),\ (2)\stackrel{(UU)}{\Longrightarrow}\ \Delta ABC \sim\Delta CAD \Rightarrow \dfrac{AC}{CD}=\dfrac{AB}{AC}=\dfrac{BC}{AD} \Rightarrow \dfrac{30}{CD}=\dfrac{AB}{30}=\dfrac{40}{25}\Rightarrow\\ \\ \\ \Rightarrow\begin{cases}\it CD=\dfrac{25\cdot30}{40}=18,75\ cm\\ \\ \\ \it AB=\dfrac{30\cdot49}{25}=48\ cm\end{cases}[/tex]
