https://file.aiquickdraw.com/mathbot/file/1727356759946pqqnv0a0.jpg

This image shows a right-angled triangle with a task to find the length of side \( XZ \), where:

- \( XY = 5.2 \, \text{mm} \)
- \( YZ = 7.8 \, \text{mm} \)
- \( \angle YXZ = 90^\circ \) (right angle).

We can use **Pythagoras' theorem** for this, which is applicable to right-angled triangles. The theorem states:

\[
XZ^2 = XY^2 + YZ^2
\]

Now, let’s calculate \( XZ \).

\[
XZ^2 = (5.2)^2 + (7.8)^2
\]
\[
XZ^2 = 27.04 + 60.84
\]
\[
XZ^2 = 87.88
\]
\[
XZ = \sqrt{87.88} \approx 9.4 \, \text{mm}
\]

So, \( XZ \approx 9.4 \, \text{mm} \) (to one decimal place).

Would you like a deeper explanation or have any further questions?

Here are 5 related questions to practice:
1. What is the formula for Pythagoras’ theorem?
2. If \( XZ = 9.4 \, \text{mm} \), what would be the area of the triangle XYZ?
3. How does Pythagoras’ theorem help in finding unknown sides in right-angled triangles?
4. If \( XY \) was 6 mm and \( YZ \) remained 7.8 mm, what would \( XZ \) be?
5. What is the significance of knowing the right angle in this triangle?

**Tip:** Always ensure that the right angle is identified before applying Pythagoras' theorem to avoid mistakes.

Find XZ correct to one decimal place given XY = 5.2 mm and YZ = 7.8 mm, where the angle YXZ is a right angle.

Solve the right-angled triangle problem using Pythagoras' theorem to find the length of XZ. Given XY = 5.2 mm and YZ = 7.8 mm, learn how to calculate XZ to one decimal place. Suitable for Grade 8-10 students.

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