\( \Large In \triangle ABC, \tan 30 ^{\circ} = \frac{BC}{40} \) => \( \Large BC = \frac{40}{\sqrt{3}} \) ...(i) \( \Large In \triangle DAB, \tan 60 ^{\circ} = \frac{BD}{40} \) => \( \Large BD = 40\sqrt{3} \) => \( \Large DC + BC = 40\sqrt{3} \) => \( \Large DC + \frac{40}{\sqrt{3}} = 40\sqrt{3} \) [from (i)] => \( \Large DC = 40 \left(\sqrt{3}-\frac{1}{\sqrt{3}}\right) = \frac{80}{\sqrt{3}} \) => \( \Large DC = 46.19 m \)