(d) 3 : 1
Let PQ and RS be the two given tower and T, the middle point of the line QS, joining the feet of the towers.
Given,
∠PTQ = 60°,∠RTS = 30°,QT = TS.
In rt. Δ PQT,
tan 60° = \(\frac{PQ}{QT}\)
⇒ \(\sqrt3\) = \(\frac{PQ}{QT}\)
⇒ QT = \(\frac{PQ}{\sqrt3}\) ...(i)
In rt. Δ RTS,
tan 30° = \(\frac{RS}{ST}\)
⇒ \(\frac{1}{\sqrt3}=\frac{RS}{ST}\)
⇒ ST = RS\(\sqrt3\) ...(ii)
From (i) and (ii),
QT = ST
⇒ \(\frac{PQ}{\sqrt3}=RS\sqrt3\)
⇒ \(\frac{PQ}{RS}=\frac{\sqrt3\times\sqrt3}{1}\)
⇒ PQ : RS = 3 : 1