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
Step 2 substitute values into the Pythagoreon therom A² + b² = c²
Step 3 solve the equation to find the missing length

Answer 1

To solve the problem involving the ladder, we can visualize the setup as a right triangle where:

- The height of the wall that the ladder reaches (11 feet) is one leg of the triangle (let's call this leg \( a \)).
- The distance from the base of the house to the bottom of the ladder is the other leg of the triangle (let's call this leg \( b \)).
- The length of the ladder (15 feet) is the hypotenuse of the triangle (let's call this \( c \)).

### Step 1: Identify the legs and hypotenuse
- \( a = 11 \) feet (the height reached on the wall)
- \( b = ? \) feet (the distance from the base of the house to the bottom of the ladder)
- \( c = 15 \) feet (the length of the ladder)

### Step 2: Substitute values into the Pythagorean theorem
The Pythagorean theorem states:
\[
a^2 + b^2 = c^2
\]

Substituting the values we have:
\[
11^2 + b^2 = 15^2
\]
Calculating \( 11^2 \) and \( 15^2 \):
\[
121 + b^2 = 225
\]

### Step 3: Solve the equation to find the missing length
Now, we can solve for \( b^2 \):
\[
b^2 = 225 - 121
\]
\[
b^2 = 104
\]

Now, taking the square root of both sides to find \( b \):
\[
b = \sqrt{104}
\]
\[
b \approx 10.20 \text{ feet}
\]

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