The angle of elevation of the top of an unfinished tower at a distance of 120 m from its base is `30^(@)`. How much higher must the tower be raised so that the angle of elevation of its top at the same point may be `60^(@)` ?

Options

A. `120 (sqrt(3)+1) m `
B. `120 (sqrt(3)-1) m`
C. `120sqrt3m`
D. 120m

Explanation

Let OA be the unfinised tower and it is to be reaised to point B Also , let C be the point of observation in the figure `(h + x )/(20) = tan 60 ^@= sqrt(3)`
`therefore h+ x = 120 sqrt(3)`
`Also ,(h)/(120)= tan 45^@ =1`
`therefore h= 120 m `
`rArr 120 + x= 120 sqrt(3)`
`rArr x= 120 (sqrt(3)-1)m `