Answer :
Answer:
Hence, the height of the ceiling at the center is 44.72 feet.
Explanation:
Consider that a whispering gallery has a length of 120 feet, and the foci are located 40 feet from the center.
Assume that the shape is a horizontal semi-ellipse with a center (0,0) and has the equation,
[tex]\frac{x^{2} }{ a^{2} } + \frac{y^{2} }{b^{2} } =1[/tex] where a>b,
so,
2a = 120
a = 60
and
c = 40
Therefore, the equation of the ellipse is,
[tex]c^{2} = a^{2} -b^{2} \\\\40^{2} = 60^{2} -b^{2}\\\\b^{2} =2000\\\\b= 44.72.[/tex]