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?

Q: 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?

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

2 : 1
√3 : 1
3 : 2
3 : 1

Correct Answer: 3 : 1

Explanation:

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

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