https://file.aiquickdraw.com/mathbot/file/1728971200789ejt2vijb.jpg

We can solve this problem using the **Pythagorean Theorem**, since the scenario forms a right triangle.

From the image:

- The **hypotenuse** (the fishing line) is 25.5 feet.
- The **vertical leg** (the difference between the total height of Victoria and the height of the water level) is \( 7 - 3 = 4 \) feet.
- The **horizontal leg** (the distance from Victoria to the fish along the water, which is the value of \( x \)) is what we're solving for.

According to the Pythagorean Theorem:
\[
a^2 + b^2 = c^2
\]
Where:
- \( a \) is the vertical leg (4 feet),
- \( b \) is the horizontal leg (which is \( x \), the distance we need to find),
- \( c \) is the hypotenuse (25.5 feet).

Now, we can substitute the known values:
\[
4^2 + x^2 = 25.5^2
\]
\[
16 + x^2 = 650.25
\]
Subtract 16 from both sides:
\[
x^2 = 650.25 - 16
\]
\[
x^2 = 634.25
\]
Now, take the square root of both sides to find \( x \):
\[
x = \sqrt{634.25} \approx 25.19 \, \text{feet}
\]

Thus, the distance from Victoria to the fish, \( x \), is approximately **25.19 feet**.

Would you like more details or have any questions?

Here are some related questions:
1. How does the Pythagorean Theorem apply to real-world scenarios like this?
2. What is the significance of each leg in the right triangle?
3. How can the accuracy of the measurements affect the result?
4. What if the fishing line was longer—how would that change the distance?
5. Can you generalize the formula to solve similar problems with different dimensions?

**Tip**: Always ensure you're identifying the correct sides of the triangle before applying the Pythagorean Theorem.

Victoria holds a fishing pole with fishing line extended according to the picture. How far is the fish from her hook? (Solve for x)

Learn how to solve a real-world problem using the Pythagorean Theorem. Victoria's fishing line forms a right triangle, and we calculate the horizontal distance to the fish using the theorem. The fishing line is 25.5 feet long, and the vertical distance from the water to the pole is 4 feet. Suitable for Grades 8-10 students.

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