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.