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)

Question

Responses

19.4 ft
19.4 ft

20.6 ft
20.6 ft

182 ft
182 ft

15.0 ft

Answer 1

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.