Question

A house painter uses a 15-foot ladder to paint the second story of a house. The ladder must reach 11 feet up the wall for the painter to reach the top of the house. How far from the base of the house should the bottom of the ladder
Step 1 identify the legs and hypotenuse of the right triangle

A = ? feet
B = 11 feet
C = 15 feet

Step 2 substitute values into the Pythagoreon therom
A² + b² = c²

Answer 1

To solve for the distance from the base of the house to the bottom of the ladder (leg A), we can follow your steps using the Pythagorean theorem:

### Given:
- Height the ladder reaches up the wall (leg B) = 11 feet
- Length of the ladder (hypotenuse C) = 15 feet

### Step 1: Identify the legs and hypotenuse
- A = distance from the base of the house to the bottom of the ladder
- B = height the ladder reaches = 11 feet
- C = length of the ladder = 15 feet

### Step 2: Substitute values into the Pythagorean theorem
Using the Pythagorean theorem:
\[
A² + B² = C²
\]
Substituting the known values:
\[
A² + 11² = 15²
\]

Calculating \( B² \) and \( C² \):
\[
A² + 121 = 225
\]

### Step 3: Solve for A
Now, isolate \( A² \):
\[
A² = 225 - 121
\]
\[
A² = 104
\]

Taking the square root of both sides to find \( A \):
\[
A = \sqrt{104}
\]
Calculating the square root:
\[
A \approx 10.20 \text{ feet}
\]

### Conclusion:
The bottom of the ladder should be approximately **10.20 feet** from the base of the house.