SOLUTION: 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 b

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: 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 b      Log On


   

Question 1066128: 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.
Answer by stanbon(75887) About Me  (Show Source):
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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.
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Coordinates of foci:: (+-c,0)
a = semi-major axis = 100 ft
b = semi-minor axis = 50 ft
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Equation::
c^2 = a^2 - b^2
c^2 = 100^2-50^2 = 7500
c = 86.60 ft
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Ans: 2c = 2*86.6 = 173.2 ft
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Cheers,
Stan H.
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