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*.

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#### Solution

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.

Concept: Heights and Distances

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