[tex]\it sinB=\dfrac{24}{25}\\ \\ \\ sinB=\dfrac{AC}{BC} \Rightarrow \dfrac{^{2)}24}{\ 25}=\dfrac{AC}{50} \Rightarrow \dfrac{48}{50}=\dfrac{AC}{50} \Rightarrow AC=48\ cm\\ \\ \\ Th.\ Pitagora\ \Rightarrow AB^2=50^2-48^2=(50-48)(50+48)=2\cdot98=\\ \\ =2\cdot2\cdot49=4\cdot49=2^2\cdot7^2 \Rightarrow AB=2\cdot7=14\ cm\\ \\ \\ \mathcal{A}=\dfrac{c_1\cdot c_2}{2}=\dfrac{14\cdot48}{2}=7\cdot48=336\ cm^2[/tex]
