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
182 ft
182 ft
19.4 ft
19.4 ft
20.6 ft
20.6 ft
15.0 ft
To solve this problem, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
In this case, the ladder forms the hypotenuse of a right-angled triangle, with one side being the height (h) above the ground where the ladder touches the house, and the other side being the distance from the bottom of the ladder to the base of the house.
The length of the ladder (hypotenuse): c = 20 feet
The distance from the base of the ladder to the house: a = 5 feet
The height we want to find is the length of the side opposite the right angle: h
Using the Pythagorean theorem:
c^2 = a^2 + h^2
Plugging in our values:
20^2 = 5^2 + h^2
400 = 25 + h^2
375 = h^2
Now, we just need to find the square root of 375 to solve for h:
h = √375 ≈ 19.4 feet (to the nearest tenth of a foot)
So the top of the ladder is touching the house approximately 19.4 feet above the ground. The correct answer is:
19.4 ft