From a point exactly midway between the foot of two towers P and Q, the angle of elevation of their tops are 30° and 60°, respectively. The ratio of the heights of tower P to that of Q is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1 : 3
Let the distance from the point to the foot of each tower be the same (since the point is exactly midway).
Height of tower P
= distance × tan 30°
= $d \times \frac{1}{\sqrt{3}}$
Height of tower Q
= distance × tan 60°
= $d \times \sqrt{3}$
Now, the ratio of heights:
$\text{P : Q} = \frac{1}{\sqrt{3}} : \sqrt{3} = 1 : 3$
Correct answer: 1 : 3