An architect wishes to design a large room 148 feet long that will be a whispering gallery. The ceiling of the room has a cross section that is an ellipse whose foci are to be located 20 feet to the right and the left of center, as shown in the following figure where d is 148 feet and x is 20 feet. 
Find the height h of the elliptical ceiling (to the nearest tenth of a foot) .
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