Question

A 12​-ft ladder is leaning against a wall and the wall is perpendicular to the ground. The base of the ladder is 8 ft from the wall. How high above the ground is the top of the​ ladder?

Answer 1

Explanation:

We can use the Pythagorean theorem to find the height above the ground where the top of the ladder is.

Let's consider the ladder as the hypotenuse of a right-angled triangle, with the wall being one side and the ground being the other side.

Let \(h\) be the height above the ground where the top of the ladder is located. We are given that the ladder is 12 ft long, and the base of the ladder (distance from the wall) is 8 ft.

According to the Pythagorean theorem, in a right-angled triangle:

h^2 = (base)^2 + (height)^2

Substitute the given values:

h^2 = 8^2 + (height)^2

Simplify:

h^2 = 64 + (height)^2

Now, let's solve for (h):

h^2 - (height)^2 = 64

Since \(h\) is positive (the height cannot be negative), we take the positive square root on both sides:

h = 64 + (height)^2

We know that the ladder is 12 ft long, so the height above the ground is:

h = 64 + (height)^2 = 64 + 12^2 = 64 + 144 = 208 approx 14.42

So, the top of the ladder is approximately 14.42 ft above the ground.