Whispering Gallery

magentarita · #1 $Old$ 10-15-2008, 01:17 PM

Jim, standing at one focus of a whispering gallery, is 6 feet from the nearest wall. His friend is standing at the other focus, 100 feet away. What is the length of this whispering gallery? How high is its elliptical ceiling at the center?

masters · #2 $Old$ 10-16-2008, 02:47 PM

Quote:

Originally Posted by magentarita $View Post$

Jim, standing at one focus of a whispering gallery, is 6 feet from the nearest wall. His friend is standing at the other focus, 100 feet away. What is the length of this whispering gallery? How high is its elliptical ceiling at the center?

See diagram.

Length of major axis = 2a = 112

a = 56

The distance from a focus to a y-intercept is also = a.

The distance from the center to a focus = c = 50.

The distance from the center to the y-intercept = b. This is what we want to find.

$b^2+c^2=a^2$

$b^2=56^2-50^2$

$b\approx25.2$ feet.

magentarita · #3 $Old$ 10-16-2008, 08:12 PM

Quote:

Originally Posted by masters $View Post$

See diagram.

Length of major axis = 2a = 112

a = 56

The distance from a focus to a y-intercept is also = a.

The distance from the center to a focus = c = 50.

The distance from the center to the y-intercept = b. This is what we want to find.

$b^2+c^2=a^2$

$b^2=56^2-50^2$

$b\approx25.2$ feet.

Another great reply!