AB and CD represent the tower and the building respectively, ∠XBD = 30° is the angle of depression. We have to calculate the measure of AC. Let it be x metres.
In right ∆BDE, DE = CA = \(x\),
BE = 117 – 37 = 80 m
∠BDE = ∠XBD = 30° (alt. ∠s)
Now, from right ∆BED, we have \(\frac{DE}{EB}\) = cot BDE
⇒ \(\frac{x}{80}\) = cot 30° ⇒ \(x\) = 80 cot 30°
⇒ \(x\) = 80√3 = 80 × 1.732 = 138.56 m.