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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. Show
each step of the solution.
To find the distance between the foci of the ellipse, we can use the formula:
c = √(a^2 - b^2)
where c is the distance between the foci, a is the semi-major axis, and b is the semi-minor axis.
Given that the length of the ellipse is 200 ft (which represents the semi-major axis) and the width is 100 ft (which represents the semi-minor axis), we can substitute these values into the formula:
c = √(200^2 - 100^2)
Simplifying,
c = √(40000 - 10000)
c = √30000
c ≈ 173.2 ft
Therefore, the distance between the foci of the ellipse is approximately 173.2 ft.