A whispering gallery is an enclosure or room where whispers can be
clearly heard in some parts of the gallery. Such a gallery can be
constructed by making its ceiling in the shape of a semi-ellipse; in this
case, a whisper from one focus can be clearly heard at the other focus. If
an elliptical whispering gallery is 90 feet long and the foci are 50 feet
apart, how high is the gallery at its center?
Answers
Answered by
12
Given : an elliptical whispering gallery is 90 feet long and the foci are 50 feet apart,
To Find : how high is the gallery at its center?
Solution:
Ellipse
x²/a² + y²/b² = 1
gallery is 90 feet long
=> 2a = 90
=> a = 45
foci are 50 feet apart
=> 2c = 50
=> c = 25
c² = a² - b²
=> 25² = 45² - b²
=> b² = 45² - 25²
=> b² = 70 * 20
=> b² = 1400
=> b = 10√14
=> b = 37.42
gallery at its center is 37.42 feet high
Learn More:
Area of the greatest rectangle inscribed in the ellipse - Brainly.in
https://brainly.in/question/14037484
area enclosed within the ellipse 5x²+2y²=80 is - Brainly.in
https://brainly.in/question/22658555
Similar questions