Use the pythagorean Theorem to solve this problem.
A painter places an 11 ft ladder against a house. The base of the ladder is 3 ft from the house. How high on the house does the ladder reach?
a^2 + b^2 = c^2
3^2 + b^2 = 11^2
Solve for b
10.6 ft
To solve this problem using the Pythagorean Theorem, we can consider the ladder as the hypotenuse of a right triangle, with the base of the ladder as one of the legs, and the height on the house as the other leg.
Given:
Base of the ladder (one leg) = 3 ft
Length of the ladder (hypotenuse) = 11 ft
Let's calculate the height on the house (other leg):
Using the Pythagorean Theorem, we have:
(Height on the house)^2 = (Length of the ladder)^2 - (Base of the ladder)^2
Substituting the given values, we have:
(Height on the house)^2 = 11^2 - 3^2
Simplifying:
(Height on the house)^2 = 121 - 9
(Height on the house)^2 = 112
Taking the square root of both sides to solve for the height:
Height on the house = √112
Height on the house ≈ 10.58 ft
Therefore, the ladder reaches approximately 10.58 ft high on the house.
To solve this problem using the Pythagorean theorem, we need to understand the relationship between the three sides of a right triangle - the ladder (hypotenuse), the base of the ladder, and the height on the house.
According to the Pythagorean theorem, the square of the length of the hypotenuse (ladder) is equal to the sum of the squares of the other two sides (base and height). In equation form, it can be written as:
c^2 = a^2 + b^2
where c is the length of the hypotenuse (ladder), and a and b are the lengths of the other two sides (base and height).
In this problem, the base of the ladder is given as 3 ft, and the length of the ladder (hypotenuse) is given as 11 ft. We need to find the height on the house.
Let's label the height on the house as h. Now we can apply the Pythagorean theorem and solve for h:
11^2 = 3^2 + h^2
121 = 9 + h^2
h^2 = 121 - 9
h^2 = 112
To find h, we take the square root of both sides:
h = √112
h ≈ 10.60 ft
Therefore, the ladder reaches a height of approximately 10.60 ft on the house.