The angle of elevation of the top of an unfinished tower

The angle of elevation of the top of an unfinished tower at a point distant 120 m from its base is 45°. If the elevation of the top at the same point is to be 60°, the tower must be raised to a height :

Let us draw the figure from the given question.
Given :- OB = h + x
In figure , we have

h + x	=	tan 60°	=	√3
120

h + x

√3 (120) ...........( 1 )

Also,	h	=	tan 45° = 1 .
	120

∴

h = 120 m

From eq. ( 1 ) ,
∴ h + x = 120 + x = 120 √3

∴

x =

120 ( √3 - 1 ) m .