This is a right triangle problem, and to find the length of the missing side, we can apply the Pythagorean theorem. The formula is:

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

Where:

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

From the diagram:

• One leg is $\sqrt{17}$,
• The hypotenuse is $9$.

We need to find the length of the other leg, which we'll call $b$.

Using the Pythagorean theorem: $(\sqrt{17})^2 + b^2 = 9^2$ $17 + b^2 = 81$ $b^2 = 81 - 17$ $b^2 = 64$ $b = \sqrt{64} = 8$

Thus, the length of the missing side is 8.

Would you like further details or explanations?

Here are five related questions to consider:

1. What is the general form of the Pythagorean theorem?
2. How do you simplify a square root in radical form?
3. Can the Pythagorean theorem be used for non-right triangles? Why or why not?
4. How would you verify if a given triangle is a right triangle using side lengths?
5. How do you calculate the perimeter of this triangle?

Tip: Always check whether the sides given correspond to the legs or hypotenuse before applying the Pythagorean theorem.