Chapter 2.4, Problem 35E

To determine

To find: the number of stories that the ladder can reach.

Answer to Problem 35E

Each story is about 10 feet, the ladder will reach $7.8$ stories

Explanation of Solution

Given:

The height of one story is 10 feet.

The bottom of the ladder will be 24 feet away from the building.

Calculation:

Let's note:

  $x=$ theheight up to which the ladder can reach

In the right triangle formed by the building, the ladder and the distance from the truck to the building, use the Pythagorean Theorem to find the expression of the distance d from the truck to the building:

  $d^2+{(x-8)}^2={74}^2$

  $d=\sqrt{5476-{(x-8)}^2}$

Now write and solve the inequality:

  $d\ge 24$

  $\sqrt{5476-{(h-8)}^2}\ge 24$

  $5476-{(h-8)}^2\ge {24}^2$

  $5476-{(h-8)}^2\ge 576$

  $5476-{(h-8)}^2+{(h-8)}^2\ge 576+{(h-8)}^2$

  $5476\ge 576+{(h-8)}^2$

  $5476-576\ge 576+{(h-8)}^2-576$

  $4900\ge (h-8^2$

  $h-8\le \sqrt{4900}$

  $h-8\le 70$

  $h\le 8+70$

  $h\le 78$

Therefore, each story is about 10 feet, the ladder will reach $\frac{78}{10}=7.8$ stories

Conclusion:

Therefore, each story is about 10 feet, the ladder will reach $7.8$ stories