To find the length of the third side in this right triangle, we will use the Pythagorean Theorem, which states:

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

Here, $a$ and $b$ are the lengths of the two legs of the triangle, and $c$ is the hypotenuse. From the diagram:

• One leg is $7$,
• The hypotenuse is $\sqrt{130}$.

We are solving for the missing side, which I will call $b$.

Using the Pythagorean Theorem:

$7^2 + b^2 = (\sqrt{130})^2$

Simplifying the equation:

$49 + b^2 = 130$

Now, subtract 49 from both sides:

$b^2 = 130 - 49$

$b^2 = 81$

Taking the square root of both sides:

$b = \sqrt{81} = 9$

So, the length of the third side is 9.

Would you like more details on the process, or have any further questions?

Here are 5 related questions:

1. How is the Pythagorean Theorem applied to non-right triangles?
2. What happens when one leg and the hypotenuse are in radical form?
3. Can the Pythagorean Theorem be used in 3D geometry?
4. How do you simplify radical expressions in different contexts?
5. What are some real-life applications of the Pythagorean Theorem?

Tip: When using the Pythagorean Theorem, always double-check whether the triangle is a right triangle.