Let's start by drawing the complete ellipse 10 meters wide.
Then we'll erase the bottom half and draw in the walls and 
floor and the places where we want to find the height at 
(2 meters from the walls).

Since it's:
>>>9 m high in the center and 6 m high at the side wall.<<<
we know that the upper covertex is 3 meters higher than the 
vertices.



a = 5, b = 3, so the equation of the whole ellipse







Now we'll erase the bottom half of the ellipse, draw in
the walls.  The floor is 6m below the vertices, so the
walls go down to the points (±5,-6). We'll draw the heights
in green 2m from the walls:



2 meters from the wall is 3 meters from the center so we
first substitute x=3 in the ellipse's equation to see how 
high above the top of the wall the ellipse is there.




Multiply through by 225




We erased the negative value, so


Then we add 6 meters to get the height from the floor.

Answer: 8.4 meters.

Edwin