The triangle in the image is a right triangle with one leg labeled as 3, the hypotenuse as 7, and the other leg, labeled as $x$, is the unknown side.

To solve for the missing side $x$, we can use the Pythagorean theorem. The theorem states:

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

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

Given:

• $c = 7$ (hypotenuse),
• $a = 3$ (one leg),
• $b = x$ (the missing leg),

We can substitute into the Pythagorean theorem:

$3^2 + x^2 = 7^2$

This simplifies to:

$9 + x^2 = 49$

Subtract 9 from both sides:

$x^2 = 40$

Now, take the square root of both sides:

$x = \sqrt{40} = \sqrt{4 \times 10} = 2\sqrt{10} \approx 6.32$

So, the missing side $x$ is approximately 6.32 units.

Would you like further details or explanations on any part of the solution?

Here are some related questions to expand on this:

1. How do we determine which side is the hypotenuse in a right triangle?
2. Can you explain how to simplify square roots, like $\sqrt{40}$?
3. What are some real-life applications of the Pythagorean theorem?
4. What happens if all three sides of the triangle are unknown?
5. How can we verify that this solution is correct?

Tip: Always double-check your solution by plugging it back into the original equation to ensure accuracy!