Question

The bottom of a ladder must be placed 4 feet from the wall. The ladder is 10 feet long How far above the ground does the ladder touch the wall?

Answer 1

To find out how far above the ground the ladder touches the wall, we can use the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

In this case, the ladder acts as the hypotenuse of a right triangle, with the distance from the bottom of the ladder to the wall as one side (4 feet) and the height we want to find as the other side. The length of the ladder is the hypotenuse.

Let's denote the height we want to find as 'h'. According to the Pythagorean theorem:

(4^2) + (h^2) = (10^2)

16 + h^2 = 100

h^2 = 100 - 16

h^2 = 84

Taking the square root of both sides:

h = √84

h ≈ 9.165

Therefore, the ladder touches the wall at a height of approximately 9.165 feet above the ground.