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).
A)128.0 feet
B)276.0 feet
C)74.3 feet
D)54.0 feet
E)71.2 feet

Question

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).
A)128.0 feet 
B)276.0 feet 
C)74.3 feet 
D)54.0 feet 
E)71.2 feet

Quizplus · Accepted Answer

Using the equation for an ellipse, we have:

c = 20
a = d/2 = 74
b = sqrt(a^2 - c^2) = sqrt(5476 - 400) = 71.2

Therefore, the height of the elliptical ceiling is 71.2 feet.

An Architect Wishes to Design a Large Room 148 Feet