Chapter 9, Problem 39RE

To determine

Find the foci of the archway such that the arch can sketch to be placed.

Answer to Problem 39RE

The foci will be $3$ feet from the center, on both sides.

Explanation of Solution

Given: It is given in the question that the arch is to set on pillars that are $10$ feet apart and is to have a height(a top the pillars) of $4$ feet.

Concept Used:

In this, use the concept of pythagoras theorem and the formula use will be $c=\sqrt{a^2-b^2}$ .

Calculation: Here, a is equal to half of the distance between the pillars, b is equal to the height of the archway stop the pillars.

  $\begin{array}{l}a=5(halfofthefulldis\tan ce)\\ b=4\end{array}$

So, use the formula of $c=\sqrt{a^2-b^2}$ , and calculate c .

  $\begin{array}{l}c=\sqrt{a^2-b^2}\\ c=\sqrt{5^2-4^2}\\ c=\sqrt{25-16}\\ c=\sqrt{9}\\ c=3\end{array}$

Conclusion:

The foci will be $3$ feet from the center, on both sides.