From a point on the ground the angle of elevation of top of a tower is is x.  On moving 'a' meters towards the tower, the elevation changes to y.  Find the height of the tower?

\(\frac{a tanx. tany}{tany − tanx}\)

tan x = \(\frac{PQ}{SQ}\)             tan y = \(\frac{PQ}{RQ}\)  

SR = SQ - RQ

⇒ a = \(\frac{PQ}{tan x}\) - \(\frac{PQ}{tan y}\) 

⇒  PQ (\(\frac{1}{tanx}\) - \(\frac{1}{tany}\)) = a

⇒  PQ = \(\frac{a tanx.tany}{tany - tanx}\)