The given problem shows a right triangle where we need to find the length of leg $x$, given the other leg is 5 units and the hypotenuse is 16 units.

We can use the Pythagorean theorem for this problem. The Pythagorean theorem states:

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

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

• One leg $a = 5$,
• The hypotenuse $c = 16$,
• We need to find the other leg $b = x$.

Using the formula:

$5^2 + x^2 = 16^2$

Now let's solve for $x$:

$25 + x^2 = 256$

Subtract 25 from both sides:

$x^2 = 256 - 25$

$x^2 = 231$

Finally, take the square root of both sides:

$x = \sqrt{231}$

Since the problem asks for the exact value, the final answer is:

$x = \sqrt{231}$

Would you like more details or have any questions on this? Here are some related questions to deepen your understanding:

1. What is the Pythagorean theorem, and how is it applied in different scenarios?
2. How can you simplify square roots like $\sqrt{231}$?
3. In what other contexts can right triangles and the Pythagorean theorem be used?
4. Can you find the length of a hypotenuse given both legs using the Pythagorean theorem?
5. What are some real-world applications of the Pythagorean theorem?

Tip: Always check if you can simplify the square root for an exact value (e.g., perfect squares).