The angles of depression of the top and the bottom of an 8 m tall building from the top of another multistoried…

Correct figure
Here, CD represents the multistoried building.
In right $\triangle DEA$
$\frac{DE}{AE} = \tan 30^\circ = \frac{1}{\sqrt{3}}$
$\Rightarrow AE = \sqrt{3} DE$ ----- (1)
In right $\triangle DCB$
$\frac{DC}{BC} = \tan 45^\circ = 1$
$\Rightarrow BC = DC$ ----- (2)
From figure, AE = BC
$\therefore \sqrt{3} DE = DC$
$\Rightarrow \sqrt{3} (DC - 8) = DC$
$\Rightarrow DC = \frac{8\sqrt{3}}{\sqrt{3}-1}$
$= \frac{8\sqrt{3}}{\sqrt{3}-1} \times \frac{\sqrt{3}+1}{\sqrt{3}+1} = (12 + 4\sqrt{3})$ m
From (2), BC = $(12 + 4\sqrt{3})$ m