Exercise 35 Page 78

We want to know how many stories of the building the fire truck's ladder can reach. Since the truck must be at least $24$ feet away from the building, this will be the maximum height. Pulling the fire truck farther away from the wall will only decrease the height reached by the ladder. Now, consider the following diagram.

Notice that the triangle formed is a right triangle. If we let $W$ be the height reached by the ladder, we can use the Pythagorean Theorem to solve for the maximum height that the ladder can reach. We know that each story is approximately $10$ feet tall, and we found that the maximum height that the ladder can reach is $70$ feet. Now we also need to consider the fact that the ladder rests on top of an $8\text{-}$foot tall fire truck. If we let $n$ be the number of stories, we can find the number of stories reached by the fire truck's ladder with an inequality. Let's solve this inequality for $n.$ The fire truck can reach up to $7.8$ stories. However, we can only have a whole number value for stories of a building and we cannot round up in this situation. Therefore, the fire truck can completely reach $7$ floors.