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The triangle you provided has sides labeled as follows:
- \( AB = 18 \)
- \( AC = 17 \)
- \( BC = x \) (the unknown)

It appears to be a right triangle with the right angle at vertex \( C \), since the problem seems to involve the use of the Pythagorean theorem. If that is correct, we can apply the Pythagorean theorem, which states:

\[
AB^2 = AC^2 + BC^2
\]

Substituting the known values:

\[
18^2 = 17^2 + x^2
\]

This simplifies to:

\[
324 = 289 + x^2
\]

Now, solve for \( x^2 \):

\[
x^2 = 324 - 289 = 35
\]

Finally, take the square root of both sides:

\[
x = \sqrt{35} \approx 5.92
\]

Thus, \( BC \approx 5.92 \).

Would you like more details or have any questions about this?

Here are 5 related questions to explore further:
1. What would happen if we changed one of the side lengths in this triangle?
2. How would you solve this problem if you didn't know it was a right triangle?
3. What is the relationship between angles in a right triangle like this one?
4. How can you apply the Pythagorean theorem in three dimensions?
5. How do different triangle properties change if you change the type of triangle (right vs. obtuse)?

**Tip:** Whenever dealing with right triangles, identifying the hypotenuse (the side opposite the right angle) helps you set up the Pythagorean theorem correctly!

In the triangle, AB = 18, AC = 17, and BC = x. Solve for x using the Pythagorean theorem.

Learn how to solve for side BC in a right triangle where AB = 18 and AC = 17 using the Pythagorean theorem. This step-by-step guide simplifies the process and helps students understand key concepts of geometry and algebra. Suitable for Grades 8-10.

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