Question

An extension ladder has a label that says, "Do not place base of

ladder less than 5 ft from the vertical surface." What is the greatest slope possible
if the ladder can safely extend to reach a height of 12 ft? Of 18 ft?

Answer 1

To determine the greatest slope possible for the extension ladder, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the height of the ladder represents one side of the right triangle, and the distance of the base of the ladder from the vertical surface represents the other side. The hypotenuse of the triangle is the length of the ladder.

Let's calculate the greatest slope possible for the ladder to reach a height of 12 ft:

Using the Pythagorean theorem:

Hypotenuse^2 = Height^2 + Base^2

Hypotenuse^2 = 12^2 + 5^2

Hypotenuse^2 = 144 + 25

Hypotenuse^2 = 169

Hypotenuse = √169

Hypotenuse = 13 ft

Now, let's calculate the greatest slope possible for the ladder to reach a height of 18 ft:

Using the Pythagorean theorem:

Hypotenuse^2 = Height^2 + Base^2

Hypotenuse^2 = 18^2 + 5^2

Hypotenuse^2 = 324 + 25

Hypotenuse^2 = 349

Hypotenuse = √349

Hypotenuse ≈ 18.66 ft

Therefore, the greatest slope possible for the ladder to reach a height of 12 ft is approximately 13 ft, and the greatest slope possible for the ladder to reach a height of 18 ft is approximately 18.66 ft.

I hope this helps! Let me know if you have any other questions.