Suggested languages for you:

Americas

Europe

Q 71.

Expert-verified
Found in: Page 655

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# Whispering Gallery: A hall $100$ feet in length is to be designed as a whispering gallery. If the foci are located $25$feet from the center, how high will the ceiling be at the center?

The height of the ceiling at the center of the gallery is $43.3feet$.

See the step by step solution

## Step 1. Given information.

The center of the ellipse be the origin and the major axis be along the x-axis.

Here, the center of the room is at $\left(0,0\right)$, It is given that the length of the room is $100feet$.

## Step 2. Height of the  ceiling at the center.

The distance from the center of the room to each vertex is $\frac{100}{2}=50feet$

The distance from center to each focus is $c=25$

Substitute $a=50$ and $c=25$ in ${b}^{2}={a}^{2}-{c}^{2}$we get.

${b}^{2}={50}^{2}-{25}^{2}\phantom{\rule{0ex}{0ex}}{b}^{2}=1875\phantom{\rule{0ex}{0ex}}b=\sqrt{1875}\phantom{\rule{0ex}{0ex}}b=43.3$

Thus, the height of the ceiling at the center of the gallery is $43.3$ feet.