https://file.aiquickdraw.com/mathbot/file/1727892598309qxigwe4h.jpg

The image shows a right-angled triangle \( \triangle FHG \), where:

- \( FH = 8 \, \text{cm} \) (one leg)
- \( HG = 13 \, \text{cm} \) (the other leg)

We are asked to calculate the hypotenuse \( FG \) using Pythagoras' theorem, which states that for a right-angled triangle:

\[
FG^2 = FH^2 + HG^2
\]

Substitute the given values:

\[
FG^2 = 8^2 + 13^2
\]
\[
FG^2 = 64 + 169 = 233
\]
\[
FG = \sqrt{233} \approx 15.26 \, \text{cm}
\]

Rounding to 1 decimal place:

\[
FG \approx 15.3 \, \text{cm}
\]

### Final Answer: \( FG = 15.3 \, \text{cm} \)

Would you like more details or have any other questions?

### Related Questions:
1. How do you apply Pythagoras' theorem to a 3D figure?
2. Can Pythagoras' theorem be used to find angles?
3. What is the relationship between the legs and hypotenuse in a 45-45-90 triangle?
4. How does the Pythagorean theorem relate to trigonometric identities?
5. How would the problem change if we only knew the hypotenuse and one leg?

### Tip:
Always check whether a triangle is a right triangle before applying Pythagoras' theorem.

Use Pythagoras' theorem to calculate the length of FG. Give your answer in centimetres (cm) to 1 d.p.

Learn how to use Pythagoras' theorem to calculate the hypotenuse FG in a right-angled triangle with sides 8 cm and 13 cm. This geometry problem applies the key formula a² + b² = c², and provides a detailed step-by-step solution, suitable for Grades 8-10.

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