Question

A 32 ft ladder rests against the side of a house. The base of the ladder is 8 ft from the house. Approximately how high above the ground is the top of the ladder?

Answer 1

Using the Pythagorean theorem, the top of the ladder is approximately 31 feet above the ground.

Step-by-step explanation:

To find out how high above the ground the top of the ladder is, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Here, the ladder serves as the hypotenuse of the triangle, and the distance from the base of the ladder to the house and the height the ladder reaches up the wall are the other two sides.

Let's denote the height the ladder reaches as 'h'. According to the Pythagorean theorem, we have:

h^2 + 8^2 = 32^2

h^2 + 64 = 1024

h^2 = 1024 - 64

h^2 = 960

h = √960

h ≈ 31 feet

Thus, the top of the ladder is approximately 31 feet above the ground.