To find the length of the third side of the right triangle, we can apply the Pythagorean Theorem, which is expressed as:

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

Where $a$ and $b$ are the two legs of the right triangle, and $c$ is the hypotenuse.

Given:

• The first leg is 7.
• The hypotenuse is 24.

We are looking for the second leg. Let’s denote it as $b$.

Using the Pythagorean Theorem:

$7^2 + b^2 = 24^2$

Simplifying:

$49 + b^2 = 576$

Now, solve for $b^2$:

$b^2 = 576 - 49$ $b^2 = 527$

Now, take the square root of both sides to find $b$:

$b = \sqrt{527}$

Calculating the square root:

$b \approx 22.9$

Thus, the length of the third side is approximately 22.9 units, rounded to the nearest tenth.

Would you like a more detailed explanation, or do you have any other questions?

Here are some related questions for further exploration:

1. What happens if you change one of the triangle's side lengths?
2. How does the Pythagorean Theorem apply to non-right triangles?
3. Can the Pythagorean Theorem be used in 3D geometry?
4. How do trigonometric ratios relate to right triangles?
5. What are the conditions for a triangle to be classified as a right triangle?

Tip: Always remember to double-check whether the triangle is a right triangle before using the Pythagorean Theorem.