Scout places his 20-ft step ladder against a house he is painting at the bottom of the ladder is 5 ft 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 a 20.6 ft b 182 ft c 15.0 ft D 19.4 ft
To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the ladder is the hypotenuse, and the distance from the base of the house to the ladder and the height from the ground to the top of the ladder are the other two sides.
Let's call the distance from the base of the house to the ladder x, and let's call the height from the ground to the top of the ladder h.
According to the problem, x = 5 ft.
We can use the Pythagorean theorem to find h:
h^2 = (20 ft)^2 - x^2
h^2 = 400 ft^2 - 5 ft^2
h^2 = 395 ft^2
h ≈ √395 ft ≈ 19.9 ft
Therefore, the top of the ladder is approximately 19.9 ft above the ground. Rounding to the nearest tenth of a foot gives us 19.9 ft. So the correct answer is D.