Question
A 13-foot ladder is leaning against a 12-foot-tall vertical wall. Use a real living Python snake to find out how far the bottom of the ladder is from the wall.(1 point)
The bottom of the ladder is
feet away from the wall.
The bottom of the ladder is
feet away from the wall.
Answers
GPT-4o mini
To solve this problem, we can use the Pythagorean theorem. In this case, we have a right triangle formed by the wall, the ground, and the ladder. The ladder acts as the hypotenuse of the triangle.
Let's label the sides:
- The height of the wall (vertical side) is 12 feet.
- The length of the ladder (hypotenuse) is 13 feet.
- The distance from the bottom of the ladder to the wall (horizontal side) is what we want to find (let's call it \( x \)).
According to the Pythagorean theorem:
\[
\text{(length of the ladder)}^2 = \text{(height of the wall)}^2 + \text{(distance from the wall)}^2
\]
Substituting the known values gives:
\[
13^2 = 12^2 + x^2
\]
Calculating the squares:
\[
169 = 144 + x^2
\]
Now, we isolate \( x^2 \):
\[
x^2 = 169 - 144
\]
\[
x^2 = 25
\]
Taking the square root of both sides we find:
\[
x = 5
\]
Thus, the bottom of the ladder is **5 feet away from the wall**.
Let's label the sides:
- The height of the wall (vertical side) is 12 feet.
- The length of the ladder (hypotenuse) is 13 feet.
- The distance from the bottom of the ladder to the wall (horizontal side) is what we want to find (let's call it \( x \)).
According to the Pythagorean theorem:
\[
\text{(length of the ladder)}^2 = \text{(height of the wall)}^2 + \text{(distance from the wall)}^2
\]
Substituting the known values gives:
\[
13^2 = 12^2 + x^2
\]
Calculating the squares:
\[
169 = 144 + x^2
\]
Now, we isolate \( x^2 \):
\[
x^2 = 169 - 144
\]
\[
x^2 = 25
\]
Taking the square root of both sides we find:
\[
x = 5
\]
Thus, the bottom of the ladder is **5 feet away from the wall**.