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
19.4 ft
19.4 ft
20.6 ft
20.6 ft
182 ft
182 ft
15.0 ft
To find the height above the ground that the top of the ladder is touching the house, we can use the Pythagorean theorem. We have a right triangle with the ladder as the hypotenuse, the distance from the base of the ladder to the house as the base, and the height we want to find as the height.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (ladder) is equal to the sum of the squares of the other two sides (distance from base to house and height):
ladder^2 = base^2 + height^2
In this case, the ladder is 20 feet, the base is 5 feet, and we want to find the height.
20^2 = 5^2 + height^2
400 = 25 + height^2
375 = height^2
Taking the square root of both sides:
height = √375
height ≈ 19.4 feet (rounded to the nearest tenth)
Therefore, the top of the ladder is touching the house approximately 19.4 feet above the ground.
To solve this problem, we can use the Pythagorean theorem. The ladder, the ground, and the wall form a right triangle.
Let's call the height of the ladder h, the distance from the bottom of the ladder to the base of the house b, and the length of the ladder l.
According to the Pythagorean theorem, l^2 = h^2 + b^2.
Given that b = 5 ft and l = 20 ft, we can substitute these values into the equation:
(20 ft)^2 = h^2 + (5 ft)^2.
Simplifying, we get:
400 ft^2 = h^2 + 25 ft^2.
Subtracting 25 ft^2 from both sides, we have:
375 ft^2 = h^2.
Taking the square root of both sides, we find:
h = √375 ft.
Round the answer to the nearest tenth of a foot:
h ≈ 19.4 ft.
Therefore, the top of the ladder is approximately 19.4 ft 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 hypotenuse (in this case, the ladder) is equal to the sum of the squares of the other two sides.
In this scenario, the ladder is the hypotenuse, the distance from the base of the house to the bottom of the ladder is one side, and the height from the ground to the top of the ladder is the other side. Let's assign variables to these values:
Hypotenuse (ladder) = 20 feet
Side 1 (distance from base to bottom of ladder) = 5 feet
Side 2 (height from ground to top of ladder) = ?
Using the Pythagorean theorem, we can set up the equation:
Side 1^2 + Side 2^2 = Hypotenuse^2
(5^2) + (Side 2^2) = 20^2
25 + (Side 2^2) = 400
Now, we can solve for Side 2:
Side 2^2 = 400 - 25
Side 2^2 = 375
Taking the square root of both sides:
Side 2 = √375
Calculating the square root of 375, we find that Side 2 is approximately 19.4.
Therefore, the height from the ground to the top of the ladder, to the nearest tenth of a foot, is 19.4 feet.