Exactly midway between the foot of two towers P and Q, the angles of elevation of their tops are 45° and 60°, respectively. The ratio of the heights of P and Q is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 1 : √ 3.
Calculations:
Height of tower P = AB
Height of tower Q = EC
D is the midpoint of BE, BD = DE
In triangle ABD,
tan 45° = AB/BD
⇒ AB = BD
In triangle CED,
tan 60° = CE/DE
⇒ CE = √3DE
⇒ CE = √3BD (BD = DE)
⇒ Required ratio = Height of tower P : Height of tower Q
⇒ AB : EC = BD : √3BD
⇒ 1 : √3