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

1 answer

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.