Question

a person in a whispering gallery standing at one focus of the ellipse can whisper and be heard by a person standing at the other focus because all the sound waves that reach the ceiling are reflected to the other person. if a whispering gallery has a length of 130 feet, and the foci are located 30 feet from the center, find the height of the ceiling at the center. round your answer to 4 decimal places. submit questionquestion 9

Answer 1

The Height of the ceiling at the center is  57.6628 feet

In geometry, an ellipse is a two-dimensional shape, that is defined along its axes. An ellipse is formed when a cone is intersected by a plane at an angle with respect to its base.

It has two focal points. The sum of the two distances to the focal point, for all the points in curve, is always constant.

The General form of ellipse is $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$

According to the question,

Length of whispering gallery is 130 feet

The foci are located 30feet from the center (0,0)

So, 2a = 130

=> a = 130/2

=> a = 65

and c = 30

As we know ,

=> c² = a² - b²

=> (30)² = (65)² - b²

=> 900 = 4225 - b²

=> b² = 4225 - 900

=> b² = 3325

=> b = 57.7 feet

Therefore , the height of the ceiling at the center is 57.6628 feet

To know more about Ellipse here

brainly.com/question/19507943

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