Question

A whispering chamber is an elliptically arched chamber. A unique feature of a whispering chamber is that when a person standing at

one focus of the ellipse whispers, he can be heard by a person standing at the other focus, regardless of the dimensions of the ellipse

from which the dome is built.

Suppose that the dimensions of the ellipse used to create a whispering dome is 200 feet by 380 feet. Walter stands at one focus, and

Barbara stands at the other focus

How far apart are Walter and Barbara?

Enter your answer, rounded to the nearest tenth of a foot in the box.

Answer 1

323.11 ft

Explanation:

The ellipse has two different axes which are the major and the minor axes. The major axis is longer than the minor axis. Therefore,

Major axis length = 2*a = 380; a = 380/2 = 190 ft

Minor axis length = 2*b = 200; b = 200/2 = 100 ft

To calculate the distance between Walter and Barbara (2*c), we consider the lengths a, b, and c as a right-angle triangle. If we use the Pythagoras theorem, we have:

c^2 = a^2 - b^2 = 190^2 - 100^2 = 26100

c = sqrt(26100) = 161.55 ft

Therefore, the distance between Walter and Barbara = 2*161.55 = 323.11 ft