Scout places his 20-foot step ladder against a house he is painting. If the bottom of the ladder is 5 feet from the base of the house, how high above the ground is the top of the ladder touching the house, to the nearest tenth of a foot?

Answer 1

We can use the Pythagorean theorem to solve this problem.

Let the height of the ladder be $h$ feet. Then, the distance from the bottom of the ladder to the point where the ladder touches the house is $h - 5$ feet.

According to the Pythagorean theorem, we have:
$(h - 5)^2 + 5^2 = 20^2$

Expanding the left side of the equation, we get:
$h^2 - 10h + 25 + 25 = 400$

Simplifying further, we have:
$h^2 - 10h - 350 = 0$

Factoring the quadratic equation, we get:
$(h - 25)(h + 15) = 0$

We can discard the negative value for $h$ since height cannot be negative.

Therefore, $h - 25 = 0$, which gives us:
$h = 25$

So, the height of the ladder is 25 feet. Thus, the top of the ladder is 25 feet above the ground. And 25 feet is the nearest whole number greater than 24.5 feet (since the height is given as a decimal).

Therefore, the top of the ladder is $\boxed{25}$ feet above the ground.

Answer 2

wrong bot gpt

Answer 3

Apologies for the incorrect response. Let's solve the problem correctly.

Using the Pythagorean theorem, we can determine the height at which the top of the ladder is touching the house.

Let the height at which the top of the ladder touches the house be represented by "h" feet.

We know that the distance from the bottom of the ladder to the base of the house is 5 feet. So, the distance from the top of the ladder to the base of the house is the total length of the ladder minus that distance, which is 20 - 5 = 15 feet.

We can form a right triangle with the base of the house, the height "h", and the length of 15 feet. According to the Pythagorean theorem:

h^2 + 15^2 = 20^2

Simplifying:

h^2 + 225 = 400

h^2 = 400 - 225

h^2 = 175

Taking the square root of both sides:

h ≈ √175

h ≈ 13.2 feet

Therefore, the top of the ladder is approximately 13.2 feet above the ground when rounded to the nearest tenth of a foot.