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The angle of elevation of the top of two vertical towers as seen from the middle point of the line joining the foot of the towers are 60° and 30° respectively. The ratio of the heights of the towers is ?
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- 2 : 1
- √3 : 1
- 3 : 2
- 3 : 1
Correct Option: D
Let AB and CD be two towers of height h1 and h2 respectively and O the mid-point of the line joining the foots A and C of the towers.
Let OA = OC = x
Then h1 = x tan 60° = x√3
and h2 = x tan 30° = x/√3
∴ h1 /h2= 3/1.
Hence, h1 : h2 = 3 : 1
