Exactly midway between the foot of two towers P and Q, the angles of elevation of their tops are 45o and 60o, respectively. The ratio of the heights of P and Q is :
Answer & explanation
Correct answer: option 1
⇒ Let the height of towers P and Q be CE and AB and D is the mid point on EB.
ED = DB
⇒ In triangle CED
⇒ tan \({45}^\circ\) = \(\frac{CE}{ED}\)
⇒ 1 = \(\frac{CE}{ED}\)
⇒ ED = CE
In triangle ADB
⇒ tan \({60}^\circ\) = \(\frac{AB}{DB}\)
⇒ \(\sqrt {3 }\) = \(\frac{AB}{DB}\)
⇒ AB = \(\sqrt {3 }\)DB or \(\sqrt {3 }\)ED
Ratio of height of tower P & Q = CE : AB = ED : \(\sqrt {3 }\)ED
⇒ 1 : \(\sqrt {3 }\)
Therefore, ratio of heights of p and Q is 1 : \(\sqrt {3 }\)