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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 178 meters, and the foci
are located 39 meters from the center, find the
height of the ceiling at the center.
OpenStax Precalculus
Height:
meters

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 wav class=

Respuesta :

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Answer:

80

Step-by-step explanation:

The height is determined by the formula

h = √(a² - b²)

where:

- a is half the length of the whispering gallery

- b is the distance from the center to the foci

Substituting these values:

h = √(89² - 39²)

h = √(7921 - 1521)

h = √6400

h = 80

So, the height of the ceiling at the center is 80 meters.

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