Yes, to find the length of $AB$ in part (c), you should use the Pythagorean theorem.

Here's how to proceed:

1. In part (b), you likely found the length of $x$ by solving for the shorter sides in the isosceles right triangle using the Pythagorean theorem.

2. For part (c), consider the larger triangle $\triangle ACB$ with $AB$ as the hypotenuse.

3. Given sides $AC = 6$ and $CB = 5$, apply the Pythagorean theorem as follows:

   $AB = \sqrt{AC^2 + CB^2} = \sqrt{6^2 + 5^2} = \sqrt{36 + 25} = \sqrt{61}$

4. Now, calculate $\sqrt{61}$ to one decimal place (as requested), which is approximately $7.8$.

Thus, the length of $AB$ is approximately 7.8 units.

Would you like more detailed steps or have any further questions?

Related Questions

1. How does the Pythagorean theorem apply to right-angled triangles?
2. How can you verify if a triangle is isosceles using side lengths?
3. What is the relationship between the hypotenuse and the legs in a right-angled isosceles triangle?
4. How does rounding affect the accuracy of your answer in geometry?
5. Why is it essential to follow the instructions for decimal places in math problems?

Tip

When working with the Pythagorean theorem, always double-check your arithmetic, especially under the square root, to avoid small calculation errors.