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.