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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).

Find the length of the leg x on the right triangle below. Enter the exact value, not a decimal approximation.

Solve for the missing leg of a right triangle where the other leg is 5 units, and the hypotenuse is 16 units using the Pythagorean theorem. Learn the step-by-step process and find the exact value, x = √231. Suitable for Grades 8-10 students.

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