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 = *blank 1* feet
B = *blank 2* feet
C = *blank 3* feet

Options for blank 2

A ?
B 15
C 11

Answer 1

To solve this problem, we can identify the legs and the hypotenuse of the right triangle formed by the ladder, the wall, and the ground.

- **A**: This represents the distance from the base of the house to the bottom of the ladder. We do not know this value yet, so we will leave this blank for now.

- **B**: This will be the length of the ladder, which is the hypotenuse of the triangle. This value is 15 feet.

- **C**: This represents the height of the ladder on the wall, which is given as 11 feet.

So we can fill in the blanks as follows:

A = *blank 1* feet (unknown, we will calculate this)
B = 15 feet (length of the ladder)
C = 11 feet (height on the wall)

Now we can summarize it:

A = *blank 1* feet
B = 15 feet
C = 11 feet

Next, you can use the Pythagorean theorem to find the distance (A) from the base of the house where the ladder touches:

\[
A^2 + C^2 = B^2
\]
\[
A^2 + 11^2 = 15^2
\]
\[
A^2 + 121 = 225
\]
\[
A^2 = 225 - 121
\]
\[
A^2 = 104
\]
\[
A = \sqrt{104}
\]
\[
A \approx 10.2 \text{ feet}
\]

So to answer your question:
- A = approximately 10.2 feet
- B = 15 feet
- C = 11 feet