To solve for $x$ in the given right triangle, we can apply the Pythagorean theorem, which states that:

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

Where:

• $a$ and $b$ are the legs of the triangle.
• $c$ is the hypotenuse (the longest side opposite the right angle).

In the triangle:

• One leg is 12.
• The other leg is $x$ (the side we need to find).
• The hypotenuse is 16.

Applying the Pythagorean theorem:

$12^2 + x^2 = 16^2$

Now, let's solve for $x$.

$144 + x^2 = 256$ $x^2 = 256 - 144$ $x^2 = 112$ $x = \sqrt{112}$ $x \approx 10.583$

Thus, the length of $x$ is approximately 10.58 units.

Would you like more details or further clarifications?

Here are 5 related questions:

1. How would you calculate the hypotenuse if both legs were given?
2. What if the triangle had a different angle? How would trigonometric functions help?
3. Can you apply the Pythagorean theorem to any triangle?
4. How do you use the Pythagorean theorem in 3D shapes?
5. How can you check if three given side lengths form a right triangle?

Tip: When dealing with square roots, simplify them when possible, or round to an appropriate decimal place based on context!