Question

The tops of two towers of heights and standing on a level ground subtend angles of 30° and 60° respectively at the centre of the line joining their feet. Then, x : y is ______.

Options

• 1 : 2

• 2 : 1

• 1 : 3

• 3 : 1

Answer 1

The tops of two towers of heights and standing on a level ground subtend angles of 30° and 60° respectively at the centre of the line joining their feet. Then, x : y is 1 : 3.

Explanation:

Let AB and CD be the given pillars and O be the midpoint of AC. 

Then, AB = x, CD = y, ∠AOB = 30° and ∠COD = 60°. 

From right ΔOAB, we have

`(OA)/(AB) = cot 30^circ`

⇒ `(OA)/x = sqrt(3)`

⇒ `OA = xsqrt(3)`   ...(i)

From right ΔOCD, we have

`(OC)/(OD) = cot 60^circ`

⇒ `(OC)/y = 1/sqrt(3)`

⇒ `OC = y/sqrt(3)`   ...(ii)

But, OA = OC.

∴ `xsqrt(3) = y/sqrt(3)`

⇒ 3x = y

⇒ `x/y = 1/3`

⇒ x : y = 1 : 3.