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?(1 point)
Responses
To solve this problem, we can use the Pythagorean Theorem.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the ladder forms a right triangle with the ground and the wall of the house. The ladder is the hypotenuse, the distance from the base of the ladder to the wall is the height, and the distance from the base of the ladder to the ground is the base.
We are given that the base of the ladder is 5 feet and the ladder is 20 feet long.
Using the Pythagorean Theorem, we can solve for the height:
height^2 + 5^2 = 20^2
height^2 + 25 = 400
height^2 = 400 - 25
height^2 = 375
Taking the square root of both sides, we find:
height ≈ √375
height ≈ 19.4
Therefore, the top of the ladder is touching the house approximately 19.4 feet above the ground.
To find the height above the ground that the top of the ladder is touching the house, we can use the Pythagorean Theorem.
The Pythagorean Theorem 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 other two sides.
In this case, the ladder forms a right-angled triangle with the ground and the house. The length of the ladder is the hypotenuse, and we know the length of one side (the distance from the house to the base of the ladder) and we want to find the length of the other side (the height above the ground).
Using the Pythagorean Theorem, we can set up the equation:
length of ladder^2 = distance from house^2 + height above the ground^2
Since the ladder is 20 feet long and the distance from the house to the base of the ladder is 5 feet, we can substitute these values into the equation:
20^2 = 5^2 + height above the ground^2
Simplifying, we get:
400 = 25 + height above the ground^2
Subtracting 25 from both sides:
375 = height above the ground^2
To find the height above the ground, we can take the square root of both sides:
sqrt(375) = sqrt(height above the ground^2)
Simplifying, we get:
19.36 = height above the ground
Therefore, the top of the ladder is touching the house at a height of approximately 19.4 feet above the ground.
To solve this problem, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right 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 other two sides.
In this case, the ladder forms a right triangle with the ground and the side of the house. The ladder is the hypotenuse, and the distance from the base of the ladder to the house is one of the other two sides.
Let's call the distance from the base of the ladder to the house "a" and the height of the ladder from the ground to the top "b". According to the Pythagorean theorem, we have the equation:
a^2 + b^2 = c^2
where c is the length of the ladder.
Given that the length of the ladder is 20 feet and the distance from the base of the ladder to the house is 5 feet, we can substitute these values into the equation:
5^2 + b^2 = 20^2
Simplifying this equation, we get:
25 + b^2 = 400
Subtracting 25 from both sides:
b^2 = 375
To solve for b, we take the square root of both sides:
b = √375
Using a calculator, we find that the square root of 375 is approximately 19.36.
So, the height of the ladder from the ground to the top, to the nearest tenth of a foot, is 19.4 feet.