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The problem you've uploaded shows a right triangle \( ABC \) with the right angle at \( C \). The triangle has the following dimensions:

- \( AB = 17 \) cm (the hypotenuse)
- \( BC = 8 \) cm (one of the legs)
- \( AC = x \) cm (the other leg, which is unknown)

We are asked to calculate the value of \( x \).

### Solution:
To solve for \( x \), we can use the **Pythagorean Theorem**, which states:
\[
AB^2 = AC^2 + BC^2
\]
Substituting the known values:
\[
17^2 = x^2 + 8^2
\]

This simplifies to:
\[
289 = x^2 + 64
\]

Next, isolate \( x^2 \) by subtracting 64 from both sides:
\[
x^2 = 289 - 64
\]
\[
x^2 = 225
\]

Finally, solve for \( x \) by taking the square root of both sides:
\[
x = \sqrt{225} = 15 \, \text{cm}
\]

### Answer:
The value of \( x \) is **15 cm**.

Would you like further details or have any questions?

### Relative Questions:
1. What is the Pythagorean Theorem, and when is it applicable?
2. How would the approach change if the hypotenuse were unknown instead?
3. Can the triangle inequality theorem verify the existence of a triangle with given sides?
4. How do you find the area of this triangle?
5. What would happen if \( BC \) was longer than the hypotenuse?

### Tip:
When working with right triangles, always consider using the Pythagorean Theorem to solve for missing sides, but ensure you correctly identify which side is the hypotenuse.

The area of triangle ABC is 1/2 cm^2. (a) Calculate the value of x.

Learn how to calculate the missing side of a right triangle using the Pythagorean Theorem. This problem involves solving for the length of side AC in triangle ABC, where AB = 17 cm, BC = 8 cm, and the area of the triangle is 1/2 cm^2. Suitable for students in Grades 8-10.

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