The image shows a right triangle where one of the legs is 6 units long, and the hypotenuse is 10 units long. We need to find the length of the other leg.

We can use the Pythagorean theorem to solve this problem, which states:

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

Where:

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

In this case:

• $a = 6$
• $c = 10$
• We need to find $b$.

Substitute the known values into the Pythagorean theorem:

$6^2 + b^2 = 10^2$ $36 + b^2 = 100$ $b^2 = 100 - 36$ $b^2 = 64$ $b = \sqrt{64}$ $b = 8$

So, the length of the third side (the other leg) is 8 units.

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

Here are some related questions:

1. What if the hypotenuse was unknown and you had to find it?
2. How do you use the Pythagorean theorem for non-right triangles?
3. How can you verify that the sides form a valid right triangle?
4. What happens if the triangle has different units, such as in feet or meters?
5. How do you apply trigonometry (sine, cosine) for angle calculations in this triangle?

Tip: The Pythagorean theorem only works for right-angled triangles. Make sure to confirm that a triangle has a right angle before applying it.