https://file.aiquickdraw.com/mathbot/file/17280717717996qlgu592.jpg

To solve this problem, we need to find the length of the guy wire. From the image, we can identify a right triangle formed by the guy wire, the distance from the pole to the stake, and the height of the pole.

### Step 1: Analyze the triangle
- The height of the pole (opposite side) is 12 feet.
- The horizontal distance (base) is the sum of the distances from the pole to the stake (2 ft) and from the pole to the tower (18 ft), giving a total of:
  \[
  18 \, \text{ft} + 2 \, \text{ft} = 20 \, \text{ft}.
  \]
  
Now we need to find the length of the guy wire, which represents the hypotenuse of this right triangle.

### Step 2: Use the Pythagorean theorem
The Pythagorean theorem states:
\[
a^2 + b^2 = c^2,
\]
where \( a \) is the height of the pole, \( b \) is the horizontal distance, and \( c \) is the length of the guy wire.

Substitute the known values:
\[
12^2 + 20^2 = c^2.
\]
This simplifies to:
\[
144 + 400 = c^2,
\]
\[
544 = c^2.
\]
Now, take the square root of both sides to find \( c \):
\[
c = \sqrt{544} \approx 23.32 \, \text{ft}.
\]

### Step 3: Round to the nearest foot
The length of the guy wire is approximately 23 feet.

### Final Answer:
The length of the guy wire is **23 feet**.

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Would you like more details on any part of this solution, or do you have any questions? 

Here are 5 related questions to further your understanding:
1. What is the Pythagorean theorem, and how does it apply to right triangles?
2. How would the length of the guy wire change if the pole were taller?
3. What is the role of the horizontal distance in calculating the hypotenuse?
4. How would the calculation differ if the total horizontal distance was measured differently?
5. Can you derive a general formula for finding the length of a guy wire in similar setups?

**Tip**: Always double-check the dimensions provided in problems like this to avoid mistakes when applying the Pythagorean theorem.

A pole 12 feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground. After placing the pole, Xin measures the distance from the pole to the stake and from the pole to the tower. The distance from the pole to the stake is 2 feet, and from the pole to the tower is 18 feet. Find the length of the guy wire, to the nearest foot.

In this problem, we find the length of a guy wire using the Pythagorean theorem. The height of the pole is 12 feet, and the horizontal distance is 20 feet. By applying the theorem, we calculate the length of the guy wire as approximately 23 feet, suitable for students in Grades 7-9.

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