The image you provided shows a right triangle with one side labeled as 7 cm (a), the other side labeled as 6 cm (b), and the hypotenuse (c) as the unknown value.

We can use the Pythagorean theorem to solve for the hypotenuse. The theorem states:

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

Where:

• $a$ is one leg of the triangle,
• $b$ is the other leg,
• $c$ is the hypotenuse.

Substituting the given values:

$7^2 + 6^2 = c^2$ $49 + 36 = c^2$ $85 = c^2$

Now, take the square root of both sides to find $c$:

$c = \sqrt{85} \approx 9.22 \, \text{cm}$

So, the length of the hypotenuse is approximately 9.22 cm.

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

Here are some related questions you might find helpful:

1. How do you apply the Pythagorean theorem in other types of triangles?
2. What is the difference between the Pythagorean theorem and the distance formula?
3. How can you use the Pythagorean theorem to find the area of a right triangle?
4. What happens if one side of a right triangle is missing and the hypotenuse is unknown?
5. Can the Pythagorean theorem be used for non-right triangles?

Tip: Always check that you have a right triangle before applying the Pythagorean theorem!