Nicholas places his 30-foot ladder against a house he is painting. If the foot of the ladder is 8 feet from the base of the house. How high above ground is the top of the ladder touching the house to the nearest tenth of a foot
We can use the Pythagorean theorem to solve this problem.
Let the height above ground where the top of the ladder touches the house be represented by 'h'.
According to the Pythagorean theorem, the square of the hypotenuse (the ladder) is equal to the sum of the squares of the two other sides (the distance from the base of the house to the foot of the ladder and the height above ground).
So, we have:
30^2 = 8^2 + h^2
900 = 64 + h^2
h^2 = 900 - 64
h^2 = 836
Taking the square root of both sides, we have:
h = √836
h ≈ 28.9 feet
Therefore, the top of the ladder is approximately 28.9 feet above the ground.