The angles of depression of the top and the bottom of a 8 m tall building from the top of a multi-storeyed building…

Correct figure
Let height of multi storeyed building AB be H m and CD is a tall building.
Let the distance between the two buildings be X m.
In $\Delta ABD$
$$\begin{aligned}& \tan 45^\circ = 1 = \frac{H}{X} \\ & \Rightarrow H = X \text{---------(i)} \\ & \text{In } \Delta AEC\end{aligned}$$
tan 30^
circ =
frac{1}{
sqrt{3}} =
frac{H-8}{X}$ \\ $X =
sqrt{3} (H-8) ---------(ii)
Solving equations (i) & (ii)
$X = 4 (3 + \sqrt{3})$
and $H = 4 (3 + \sqrt{3})$
The height of the multi storeyed building is $4 (3 + \sqrt{3})$ m and the distance between the two buildings is $4 (3 + \sqrt{3})$ m.