https://file.aiquickdraw.com/mathbot/file/1731403082660hlv8pzh3.jpg

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.

Learn how to apply the Pythagorean theorem to calculate the hypotenuse and side lengths in right-angled triangles. This problem involves calculating the length of AB using known side lengths AC = 6 and CB = 5, with the answer rounded to one decimal place. Suitable for students in Grades 7-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation