Question

A 10-foot ladder is leaning against a wall. The bottom of the ladder is 4 feet from the base of the wall, as shown below.

What is the closest distance from the top of the ladder to the base of the wall?

Answer 1

The closest distance from the top of the ladder to the base of the wall is approximately 9.165 feet.

Step-by-step explanation:

To find the closest distance from the top of the ladder to the base of the wall, we can use the Pythagorean theorem. The ladder, the wall, and the ground form a right triangle. The length of the ladder (hypotenuse) is 10 feet, and the distance from the base of the ladder to the wall (adjacent side) is 4 feet. Let's call the distance from the top of the ladder to the base of the wall 'x'.

Using the Pythagorean theorem, we have:
x^2 + 4^2 = 10^2
x^2 + 16 = 100
x^2 = 84
x = √84 ≈ 9.165

So, the closest distance from the top of the ladder to the base of the wall is approximately 9.165 feet.