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
By using the Pythagorean theorem, we can determine the height at which the top of the ladder touches the house.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the height of the ladder is the hypotenuse, and the distance from the bottom of the ladder to the base of the house is one of the other two sides. We can label the distance from the bottom of the ladder to the base of the house as "a" and the height of the ladder as "b".
Using the Pythagorean theorem, we have:
a^2 + b^2 = c^2
where c is the height of the ladder.
Plugging in the given values, we have:
5^2 + b^2 = 20^2
25 + b^2 = 400
b^2 = 400 - 25
b^2 = 375
To find the value of b, we take the square root of both sides:
b = √375 ≈ 19.36
Therefore, the top of the ladder is approximately 19.36 feet above the ground.