5 m high pole stands on a building of height 25 m. The pole and the building subtend equal angles at an antenna placed at a height of 30 m. The distanceo f the antenna from the top of the pole is

Options

A. `5 sqrt(2/3)`
B. `(5sqrt(3))/2`
C. `5sqrt(3/2)`
D. `5sqrt(6)`

Explanation

Let AB be the pole standing on the building BC and O be the position of the antenna .

In triangle OAB ,
`tanalpha =5/x` …(1)
In triangle OAC ,
`tan2alpha = (30)/x` ...(2)
From (1) and (2) .
`tan2alpha = 6tanalpha `
`rArr 3-3tan^2alpha =1`
`rArr tanalpha = sqrt((2)/(3))`
From (1) , `x= 5cotalpha =5sqrt((3)/(2))`