The base of an auditorium is in the form of an ellipse 200 ft. long and 100 ft. wide. a pin dropped near one focus can clearly be heard at the other focus. determine the distance between the foci to the nearest tenth of a foot

The ellipse has major axis of 200 ft and minor axis of 100 ft
The semi major axis, a = 100 ft
The semi minor axis, b = 50 ft
The distance from the center to the focus, c, is calculated using
a² = b² + c²
Substituting and solving for c
c = 86.60 ft
The distance between the two focci is twice the value of c
2(86.60) = 173.21 ft