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To calculate the length of side \( FG \) in the right triangle using Pythagoras' Theorem, we use the formula:

\[
c^2 = a^2 + b^2
\]

Here:
- \( a = 9 \, \text{cm} \) (side \( HF \)),
- \( b = 19 \, \text{cm} \) (side \( HG \)),
- \( c \) is the hypotenuse (side \( FG \)).

### Step-by-step calculation:

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

\[
FG^2 = 9^2 + 19^2
\]

\[
FG^2 = 81 + 361 = 442
\]

Now, taking the square root of both sides:

\[
FG = \sqrt{442} \approx 21.0 \, \text{cm}
\]

So, the length of side \( FG \) is approximately **21.0 cm**, rounded to 1 decimal place.

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Do you need further clarification or have any questions?

Here are some related questions to expand your understanding:
1. How would you calculate the length of \( HG \) if only \( FG \) and \( HF \) were given?
2. Can you use the Pythagorean theorem in non-right triangles?
3. What is the general formula for finding the area of a right triangle?
4. How does the Pythagorean theorem relate to trigonometric ratios?
5. Can you determine the angle \( H \) using the given sides?

**Tip**: Always check whether a triangle is right-angled before applying the Pythagorean theorem.

Use Pythagoras' theorem to calculate the length of FG. Give your answer in centimetres (cm) to 1 d.p. The right triangle has sides HF = 9 cm, HG = 19 cm, and FG is the hypotenuse.

Learn how to calculate the length of side FG in a right triangle using Pythagoras' theorem. This example involves a right triangle with sides HF = 9 cm and HG = 19 cm. Discover the step-by-step method and the final answer rounded to 1 decimal place.

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