The image depicts a right triangle, and we are asked to find the length of the missing side labeled with a question mark (?). We will apply the Pythagorean theorem here since we know this triangle involves two sides and a hypotenuse.

The Pythagorean theorem is given by:

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

Where:

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

From the image:

• One leg is 9 units,
• The hypotenuse (opposite the right angle) is 41 units,
• We are solving for the other leg (the missing side).

Let's denote the missing side as $b$. Applying the Pythagorean theorem:

$9^2 + b^2 = 41^2$

$81 + b^2 = 1681$

$b^2 = 1681 - 81 = 1600$

$b = \sqrt{1600} = 40$

Thus, the length of the missing side is $\boxed{40}$.

Would you like more details or have any further questions?

Related Questions:

1. How would the result change if the hypotenuse were 50 units instead of 41?
2. Can we find the missing side if the other leg and the hypotenuse are given as decimals?
3. How can the Pythagorean theorem be applied in three-dimensional problems?
4. What if both legs of the triangle are unknown, but the hypotenuse and the area are given?
5. How would this problem change if it were not a right triangle?

Tip:

Always ensure that the triangle is a right triangle before applying the Pythagorean theorem.