From the points 'x' m and 'y' m away from the foot of a tree on either side of it the angles of elevation of the tree-top are $$ \alpha , \beta $$ respectively. If $$ \alpha +  \beta = 90^\circ $$, then find the height of the tree.

A

$$ x \cos \alpha + y \cos\beta $$

B

$$ \sqrt{xy}  $$

C

$$ \frac {(x+y)^2}{2} $$

D

$$ (x-y)^2  $$