A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height h. At a point on the plane the angles of elevation of the bottom and top of the flagstaff are θ and 2θ respectively. What is the height of the tower ?

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NDA 01/2022: Maths Previous Year paper (Held On 10 April 2022)
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  1. h cos θ
  2. h sin θ
  3. h cos 2θ
  4. h sin 2θ

Answer (Detailed Solution Below)

Option 3 : h cos 2θ
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NDA 01/2025: English Subject Test
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Detailed Solution

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Given:

flagstaff of height h is surmounted on a verticle tower.

Angles of elevation of the bottom and top of the flagstaff are θ and 2θ respectively.

Formula used:

1. tan θ = Perpendicular/Base

2. tan 2θ =

3. cos 2θ = 

 

Calculation:

Let the height of the tower be x.

In right triangle ABC

tan θ = AC/AB = x/AB

⇒ AB = x/tan θ          ------(1)

In right triangle ABD

tan 2θ = AD/AB = (x + h)/AB

⇒  = (x + h)/AB   [Using formula (2)]

⇒  =      [From equation (1)]

⇒  =  

⇒ 

⇒  

⇒   

⇒  = cos2θ       [Using formula (3)]

⇒ x = hcos 2θ 

∴ The height of the tower is h cos 2θ 

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