Find the length of line DC

By pythagorean theorem, we have

$AD=\sqrt{24^2+32^2}=40$

$\sin \angle EDA=\dfrac{32}{40}$ $\implies$ $\angle EDA=\sin^{-1}\left(\dfrac{32}{40}\right)$

$\tan \angle BDA=\dfrac{9}{40}$ $\implies$ $\angle BDA=\tan^{-1}\left(\dfrac{9}{40}\right)$

$\angle EDC=\angle EDA - \angle BDA=\sin^{-1}\left(\dfrac{32}{40}\right)-\tan^{-1}\left(\dfrac{9}{40}\right)$

$\cos \angle EDC=\dfrac{24}{DC}$

$DC=\dfrac{24}{\cos \angle EDC}=\dfrac{24}{\cos\left[\sin^{-1}\left(\dfrac{32}{40}\right)-\tan^{-1}\left(\dfrac{9}{40}\right)\right]} \approx$ $\boxed{31.53846}$