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To solve the problem, we need to find the length of side \( x \) in the right triangle using the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (\( c \)) is equal to the sum of the squares of the lengths of the other two sides (\( a \) and \( b \)):

\[
c^2 = a^2 + b^2
\]

In the triangle provided:
- The hypotenuse \( c = 62 \)
- One leg \( a = 41 \)
- The other leg \( b = x \)

We need to solve for \( x \):

\[
62^2 = 41^2 + x^2
\]

Calculating the squares:

\[
3844 = 1681 + x^2
\]

Subtract 1681 from both sides to isolate \( x^2 \):

\[
3844 - 1681 = x^2
\]

\[
2163 = x^2
\]

Now, take the square root of both sides:

\[
x = \sqrt{2163}
\]

Calculating the square root:

\[
x \approx 46.5
\]

So, the length of \( x \) is approximately \( 46.5 \).

Would you like further details or have any questions about this solution?

Here are some related questions to consider:
1. How does the Pythagorean theorem apply to non-right triangles?
2. Can you find the length of the hypotenuse if both legs are known?
3. What are some real-life applications of the Pythagorean theorem?
4. How does trigonometry relate to the Pythagorean theorem?
5. What happens to the formula if the triangle sides are not integers?

**Tip:** The Pythagorean theorem only applies to right-angled triangles, so always verify the angle before applying it.

Solve for x in a right triangle where the hypotenuse is 62 units and one leg is 41 units.

Learn how to solve for the missing side in a right triangle using the Pythagorean theorem. In this problem, the hypotenuse is 62 units, and one leg is 41 units. The solution includes a step-by-step calculation, making it suitable for students in Grades 8-10.

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