Let AB be a five-storey building, from the rooftop point A, the angle of elevation to the top of the monument (point C) is 45°, and the angle of depression to the base of the monument (point D) is 60°. The height of the building AB = 18 meters. Assume AE ∥ BD. So, ∠CAE = 45° ∠EAD = 60° ∴ ∠ADB = ∠EAD = 60° From right-angled triangle ABD: \[ \tan 60^\circ = \frac{AB}{BD} = \frac{18}{BD} \Rightarrow \sqrt{3} = \frac{18}{BD} \Rightarrow BD = \frac{18}{\sqrt{3}} = \frac{18\sqrt{3}}{3} = 6\sqrt{3} \] ∴ AE = BD = \(6\sqrt{3}\) From right-angled triangle AEC: \[ \tan 45^\circ = \frac{CE}{AE} = \frac{CE}{6\sqrt{3}} \Rightarrow 1 = \frac{CE}{6\sqrt{3}} \Rightarrow CE = 6\sqrt{3} \] Now, \[ CD = CE + ED = CE + AB = 6\sqrt{3} + 18 = 6 \times 1.732 + 18 = 10.392 + 18 = 28.392 \] ∴ The height of the monument is 28.392 meters