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.