https://file.aiquickdraw.com/mathbot/file/172687501653200q388fz.jpg

The diagram shows a right triangle, where we are given two sides:
- \( AB = 9 \)
- \( AC = 6 \)

To find the distance \( BC \), we can use the Pythagorean theorem, which applies to right-angled triangles:

\[
AB^2 = AC^2 + BC^2
\]

Rearranging this equation to solve for \( BC \):

\[
BC^2 = AB^2 - AC^2
\]

Now let's substitute the known values:

\[
BC^2 = 9^2 - 6^2
\]
\[
BC^2 = 81 - 36 = 45
\]

Therefore:

\[
BC = \sqrt{45} = 3\sqrt{5} \approx 6.71
\]

So, the distance \( BC \) is approximately **6.71 units**.

Would you like further details or have any questions? Here are five related questions to expand on this:

1. How would the Pythagorean theorem change if the triangle was not a right triangle?
2. Can you calculate the area of the triangle with the known side lengths?
3. What would happen if \( AC \) and \( BC \) were swapped? How would the calculation differ?
4. Can you explore different methods for calculating the distance between points in non-right triangles?
5. How can trigonometric ratios be used to find unknown sides in right triangles?

**Tip:** When using the Pythagorean theorem, always ensure you know which side is the hypotenuse (the longest side opposite the right angle).

What is the distance BC given AB = 9 and AC = 6? The diagram is of a right triangle.

Learn how to calculate the distance BC in a right triangle where AB = 9 and AC = 6. This problem involves the Pythagorean Theorem and is suitable for students in Grades 8-10.

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