Question

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

Answer 1

Let AB and CD be the two towers of heights x and y, respectively.

Suppose E is the centre of the line joining the feet of the two towers i.e. BD.

Now, in ∆ABE,

`(AB)/(BE)=tan30^@`

`=>x/(BE)=1/sqrt3`

`=>BE=sqrt3x"  ....(1)"`

Also

In ∆CDE,

`(CD)/(DE)=tan60^@`

`=>y/(DE)=sqrt3`

`=>DE=y/sqrt3"....(2)"`

Now, BE = DE   .....(3)       (E is mid-point of BD.)

So, from (1), (2) and (3), we get

`sqrt3x= y/sqrt3`

`=>x/y=1/3`

Hence, the ratio of x and y is 1 : 3.