The given image shows a right triangle with one of the sides labeled as 3, another side as 7, and the right angle indicated by the square. To find the length of the third side, we can apply the Pythagorean Theorem, which states:

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

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

From the diagram:

• One leg is 3.
• The other leg is 7.
• The hypotenuse is unknown, so we will solve for it.

Let's calculate the length of the third side (hypotenuse).

$a^2 + b^2 = c^2$ $3^2 + 7^2 = c^2$ $9 + 49 = c^2$ $58 = c^2$ $c = \sqrt{58} \approx 7.6$

Therefore, the length of the hypotenuse is approximately 7.6 units.

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

Here are some related questions to explore:

1. How would the Pythagorean Theorem apply if the given side lengths were different?
2. How can you determine if a triangle is a right triangle just by looking at the side lengths?
3. What happens if the given sides form an acute or obtuse triangle?
4. How can trigonometry be used to solve for unknown sides of a right triangle?
5. What are some real-world applications of the Pythagorean Theorem?

Tip: The Pythagorean Theorem is only applicable to right-angled triangles!