Final answer:
To determine the minor axis length for an elliptical whisper chamber with a major axis of 30 ft and foci 4 ft from the center, one can use the relationship c^2 = a^2 - b^2. After calculating, we find the minor axis length should be approximately 14.5 ft, making the correct answer C. 14.5 ft.
Step-by-step explanation:
The problem question involves designing a whisper chamber in the shape of an ellipse, using the warehouse space with a major axis of 30 ft and placing the chamber's foci 4 ft from the center. To determine how far out from the center along the minor axis the chamber should be built, we need to use the properties of an ellipse.
An ellipse is defined by the equation (x/a)^2 + (y/b)^2 = 1, where 2a is the length of the major axis, and 2b is the length of the minor axis. The distance between the center and a focus is 'c', and it relates to a and b via the equation c^2 = a^2 - b^2. Given that c, or the focal distance, is 4 ft and the length of the major axis is 30 ft (a = 15 ft), we can find b by solving c^2 = a^2 - b^2.
Let's calculate: c^2 = 4 ft * 4 ft = 16 ft^2; a^2 = 15 ft * 15 ft = 225 ft^2; thus 225 ft^2 - 16 ft^2 = b^2, which gives us 209 ft^2 = b^2. Then, b = sqrt(209 ft^2) which is approximately 14.5 ft. So, the chamber should be built out 14.5 ft from the center along the minor axis to maximize the whispering effect. The correct choice is C. 14.5 ft.