To find the hypotenuse of a right triangle when the lengths of the two legs are given, we can use the Pythagorean Theorem. The theorem states:

$c = \sqrt{a^2 + b^2}$

Where:

• $c$ is the hypotenuse,
• $a$ and $b$ are the legs of the triangle.

In this case, one leg $a = 9 \, \text{cm}$ and the other leg $b = 8 \, \text{cm}$.

Let's calculate the hypotenuse.

$c = \sqrt{9^2 + 8^2} = \sqrt{81 + 64} = \sqrt{145} \approx 12.04 \, \text{cm}$

Rounded to the nearest tenth, the hypotenuse is:

$c \approx 12.0 \, \text{cm}$

Would you like more details or have any further questions?

Here are 5 related questions to further your understanding:

1. What is the Pythagorean Theorem, and why does it work?
2. How can you determine if a triangle is a right triangle using the side lengths?
3. If one leg of a right triangle is doubled, how would the hypotenuse change?
4. How do you find the area of a right triangle if you know the leg lengths?
5. Can the Pythagorean Theorem be applied to non-right triangles?

Tip: When solving right triangle problems, always check if the triangle is a special one (like a 3-4-5 triangle) to simplify your calculations.