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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.
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.
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