This is a right-angled triangle problem, and we can solve for the length of FG using Pythagoras' theorem, which states:

$a^2 + b^2 = c^2$

where $c$ is the hypotenuse (the side opposite the right angle), and $a$ and $b$ are the other two sides.

In this triangle:

• $FH = 8 \, \text{cm}$ (one leg)
• $HG = 13 \, \text{cm}$ (the other leg)
• $FG = c$ (the hypotenuse we are solving for)

Now, applying Pythagoras' theorem:

$FG^2 = FH^2 + HG^2$

Let me calculate the length of FG.The length of $FG$ is approximately $15.3 \, \text{cm}$ (to 1 decimal place).

Would you like more details or have any questions about this?

Here are 5 related questions to explore further:

1. How would you calculate the area of this triangle?
2. Can you use trigonometry to find the angles of this triangle?
3. How does Pythagoras' theorem apply in three-dimensional shapes?
4. What are the limitations of Pythagoras' theorem in non-Euclidean geometry?
5. How can you verify the accuracy of your result using a different method?

Tip: Always check that the side lengths provided match the conditions of a right-angled triangle before applying Pythagoras' theorem.