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To calculate the length of \( YZ \) using Pythagoras' theorem, we can apply the following steps:

Given:
- \( XY = 5 \, \text{cm} \)
- \( XZ = 17 \, \text{cm} \)

In this right-angled triangle, \( YZ \) is the hypotenuse, and \( XY \) and \( XZ \) are the two legs of the triangle.

According to Pythagoras' theorem:
\[
YZ^2 = XY^2 + XZ^2
\]

Substituting the given values:
\[
YZ^2 = 5^2 + 17^2
\]
\[
YZ^2 = 25 + 289 = 314
\]

Now, take the square root of both sides to find \( YZ \):
\[
YZ = \sqrt{314} \approx 17.7 \, \text{cm}
\]

Therefore, the length of \( YZ \) is approximately \( 17.7 \, \text{cm} \) to 1 decimal place.

Would you like further details or have any questions?

Here are 5 related questions you might want to explore:
1. How is Pythagoras' theorem used to find distances in real-world applications?
2. What other methods can be used to calculate the sides of a right triangle?
3. Can you prove Pythagoras' theorem?
4. How do you calculate the area of a right-angled triangle using its sides?
5. What is the relationship between Pythagoras' theorem and trigonometry?

**Tip**: When solving geometry problems involving right triangles, always double-check if the triangle is a right triangle before applying Pythagoras' theorem.

Using Pythagoras' theorem, calculate the length of YZ. Give your answer to 1 d.p. The sides given are XY = 5 cm and XZ = 17 cm.

Learn how to apply Pythagoras' theorem to calculate the hypotenuse of a right-angled triangle where the sides are 5 cm and 17 cm. Suitable for students in Grades 7-9.

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