Chapter 10.3, Problem 73AYU

To determine

To find: A suitable rectangular coordinate system and the height of the arch at distances of 10,30, and 50 feet from the center of the semielliptical arch.

Answer to Problem 73AYU

High of the ceiling is $25.2$ .

Explanation of Solution

Given:Thespan of a bridge is 120 feet and maximum height is 25 feet.

It is given that thespan of a bridge is 120 feet and maximum height is 25 feet and this bridge is built in the shape of a semielliptical arch.

  $\begin{array}{l}h=0\\ k=0\\ a=50\\ c=25\end{array}$

Now equation of the ellipse is

  $\begin{array}{l}\frac{x^2}{{56}^2}+\frac{y^2}{{56}^2-{50}^2}=1\\ \frac{x^2}{3136}+\frac{y^2}{636}=1\end{array}$

Hence, high of the ceiling is $\sqrt{636}=25.2$