Nicholas places his 30 foot ladder against a house he is painting if the foot of the ladder is 8 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
We can use the Pythagorean theorem to solve this problem.
Let's assume that the height of the ladder where it touches the house is "h".
According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the ladder in this case) is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is 30 ft, the base is 8 ft, and the height is "h". Therefore, we can write the equation:
(8^2) + (h^2) = (30^2)
Simplifying, we have:
64 + h^2 = 900
Subtracting 64 from both sides of the equation:
h^2 = 836
Taking the square root of both sides:
h ≈ √836
h ≈ 28.9 ft
Therefore, the top of the ladder is touching the house at a height of approximately 28.9 feet above the ground.