SOLUTION: In advance, thank you for trying to help! In a room shaped like an ellipse, something whispered at 1 focus can be clearly heard at the other focus. The U.S. Capitol National Statu

Question 1140779: In advance, thank you for trying to help!
In a room shaped like an ellipse, something whispered at 1 focus can be clearly heard at the other focus. The U.S. Capitol National Statuary Hall in Washington, D.C. is such a whispering gallery. From 1807 to 1857, the U.S. House of Representatives met in this room. According to legend, when John Quincy Adams was a representative following his presidency, he used to look as though he was asleep at his desk during debate, but he was listening to what representatives of the opposing party on the other side of the room were whispering. If the elliptical pattern of this whispering gallery is 92 feet long by 58 feet wide, how far from the whisperer at 1 focus is the listener at the other focus?
Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
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Each of the two focuses of an ellipse is located on its major axis at the distance of  c =  from its center,


where "a" is the major semi-axis of the ellipse and "b" is its minor semi-axis.



In the given case,  a =  = 46 ft,  b =  = 29 ft,  so


the distance from the center of the ellipse to any of the two its focuses is


    c =  = 35.707 ft.


The distance between the focuses is two times this value, i.e.  2*35.707 = 71.14 ft.     ANSWER

Solved.

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For this and other remarkable properties of ellipses see the lessons
    - Ellipse definition, canonical equation, characteristic points and elements
    - Ellipse focal property
    - Tangent lines and normal vectors to a circle
    - Tangent lines and normal vectors to an ellipse
    - Optical property of an ellipse
    - Optical property of an ellipse revisited
in this site.

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