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
20.6 ft
20.6 ft
15.0 ft
15.0 ft
182 ft
182 ft
19.4 ft
To solve this problem, we can use the Pythagorean theorem. The ladder, the distance from the base of the house to the bottom of the ladder, and the height from the ground to the top of the ladder form a right triangle.
We can label the bottom of the ladder as the length of the triangle leg and the height from the ground to the top of the ladder as the height of the triangle leg.
Using the Pythagorean theorem, we have:
(Height of ladder)^2 = (Distance from the base of the house to the bottom of the ladder)^2 + (Length of the ladder)^2
(Height of ladder)^2 = 5^2 + 20^2
(Height of ladder)^2 = 25 + 400
(Height of ladder)^2 = 425
Height of ladder = √425
Height of ladder ≈ 20.6155 ft
Therefore, the height above the ground where the top of the ladder touches the house is approximately 20.6 ft.
To find the height at which the top of the ladder is touching the house, we can use the Pythagorean theorem.
According to the theorem:
c^2 = a^2 + b^2
In this case, the ladder is the hypotenuse (c), the distance from the base of the ladder to the house is one of the legs (a), and the height we want to find is the other leg (b).
Let's substitute the values into the formula:
c^2 = a^2 + b^2
20^2 = 5^2 + b^2
400 = 25 + b^2
375 = b^2
Now, we'll find b by taking the square root of both sides of the equation:
b = sqrt(375)
b ≈ 19.4 ft
Therefore, the top of the ladder touches the house at a height of approximately 19.4 feet above the ground. So the answer is 19.4 ft.
To find the height of the ladder touching the house, we can use the Pythagorean theorem. The theorem states that in a right-angled triangle, the square 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 the hypotenuse, the distance from the base of the ladder to the house forms one side, and the height of the ladder touching the house forms the other side.
Using the Pythagorean theorem, we can calculate:
c^2 = a^2 + b^2
Where c is the length of the ladder, a is the distance from the base of the ladder to the house, and b is the height of the ladder touching the house.
In this case, c = 20 ft, a = 5 ft. Let's solve for b:
20^2 = 5^2 + b^2
400 = 25 + b^2
375 = b^2
b = sqrt(375)
b ≈ 19.4 ft
Therefore, the height of the ladder touching the house is approximately 19.4 feet.