Question

The tops of two towers of height x and y, standing on level ground, subtend angles of 30º and 60º respectively at the centre of the line joining their feet, then find x : y.        

Answer 1

Let AB and CD be the two towers and E be the mid-point of AC.
Height of the tower, AB = y
Height of the tower, CD = x 

it is given that, ∠ AEB=60° and ∠ CED=30°

Also, `AE=EC`

In right Δ AEB, 

`tan 60°= (AB)/(AE)`

⇒ `sqrt3=y/(AE)` 

`⇒ AE=y/sqrt3`

In right ∆CED, 

`tan 60° = (AB)/(AF)` 

⇒ `1/sqrt3=x/(CE)`

`⇒CE=sqrt3x` 

`y/sqrtx=sqrt3x`

`⇒ y=3x`

`⇒x/y=1/3`

`∴ x: y=1:3`

Hence, the ratio of x : y is 1 : 3.