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The angle of depression of a 37 m high building from the top of a tower 117 m high is 30°. Calculate the distance between the building and the tower.

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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.

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