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 = 11 feet
B = ? Feet
C = 15 feet

Step 2: substitute values into the Pythagoreon therom a² + b² = c²
11² + ?² = 15²

Step 3: solve the equation to find the missing length

121 + b² = 225

To solve the equation, we need to get the variable by itself. We do this by square rooting how much from both sides
A 224
B 121
C b²

Answer 1

It looks like you're on the right path to solving the problem using the Pythagorean theorem. Let's go through the steps carefully to find how far from the base of the house the bottom of the ladder should be placed.

**Step 1: Identify the legs and hypotenuse of the right triangle.**

In your scenario:
- **A** (height the ladder reaches up the wall) = 11 feet
- **B** (distance from the base of the house to the bottom of the ladder) = ?
- **C** (length of the ladder) = 15 feet

**Step 2: Substitute values into the Pythagorean theorem \( a^2 + b^2 = c^2 \)**

Using the values we have:
\[
11^2 + b^2 = 15^2
\]

This simplifies to:
\[
121 + b^2 = 225
\]

**Step 3: Solve the equation to find the missing length.**

To isolate \( b^2 \):
\[
b^2 = 225 - 121
\]
\[
b^2 = 104
\]

Now take the square root of both sides to find \( b \):
\[
b = \sqrt{104}
\]

Calculating \( \sqrt{104} \):
\[
b \approx 10.2 \text{ feet}
\]

Thus, the bottom of the ladder should be approximately **10.2 feet** from the base of the house.