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Math Help - Whispering Gallery

  1. #1
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    Whispering Gallery

    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?
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  2. #2
    A riddle wrapped in an enigma
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    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.
    Attached Thumbnails Attached Thumbnails Whispering Gallery-ellipse.bmp  
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  3. #3
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    ok....

    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!
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