Let A and B be two towers with the same base. From the mid point of the line joining their feet, the angles of elevation of the tops of A and B are 30° and 45°, respectively. The ratio of the heights of A and B is :
Answer & explanation
Correct answer: option 2
In triangle RTS
⇒ tan\({30}^\circ\) = \(\frac{RS}{ST}\)
⇒ \(\frac{1}{√3}\) = \(\frac{RS}{ST}\)
⇒ RS = \(\frac{ST}{√3}\)
In triangle PTQ
⇒ tan\({45}^\circ\) = \(\frac{PQ}{QT}\)
⇒ 1 = \(\frac{PQ}{QT}\)3
⇒ PQ = QT
As QT = ST
⇒ √3 RS = PQ = A : B = 1 : √3
Therefore, ratio of towers A and B is 1 : √3.