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In the given problem, we are dealing with a right-angled triangle \(ABC\), where:

- \(|AB| = 34\) (one of the legs of the triangle),
- \(|AC| = 43.36\) (the hypotenuse),
- We are tasked with finding the length of \(|BC|\), the other leg, to two decimal places.

### Solution:

Using the **Pythagorean theorem**, we know that in any right-angled triangle:

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

We can rearrange this formula to solve for \(|BC|\):

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

Substitute the given values:

\[
BC^2 = 43.36^2 - 34^2
\]

Let me calculate this for you.The length of \(|BC|\) is approximately \(26.91\), correct to two decimal places.

Would you like further details or clarifications on this solution? Here are five related questions to explore:

1. How does the Pythagorean theorem work for non-right triangles?
2. Can the Pythagorean theorem be used in 3D geometry?
3. What are the applications of right triangles in real-world problems?
4. How do you determine which side is the hypotenuse in a right triangle?
5. What other methods can be used to solve triangles besides the Pythagorean theorem?

**Tip:** Always ensure that your triangle is a right triangle before applying the Pythagorean theorem.

In the right-angled triangle shown, |AB| = 34 and |AC| = 43.36. Find the length |BC| correct to two decimal places.

Learn how to find the length of side BC in a right-angled triangle where |AB| = 34 and |AC| = 43.36 using the Pythagorean theorem. This problem covers key geometry concepts and is suitable for students in Grades 8-10.

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