Decide which given side is the hypotenuse and which is the leg, then plug them into $a^2 + b^2 = c^2$ using a variable for the unknown leg.

After substituting the values, rearrange the equation so the variable's square is alone on one side, then think about how to undo squaring.

Be careful computing $17^2$ and subtracting $64$ from it; a small arithmetic mistake will lead to one of the incorrect answer choices.

In Desmos, type sqrt(17^2 - 8^2) to represent the unknown leg using the Pythagorean theorem $x = \sqrt{c^2 - a^2}$.

Look at the numerical result that Desmos shows for sqrt(17^2 - 8^2) and match that value to the closest answer choice given.

Because this is a right triangle and you know two sides (a leg and the hypotenuse), use the Pythagorean theorem:

Here, $c$ is the hypotenuse, and $a$ and $b$ are the legs.

Let the unknown leg be $x$. You are given that one leg is $8$ and the hypotenuse is $17$, so plug into the formula:

Now compute the squares:

• $8^2 = 64$
• $17^2 = 289$

So the equation becomes:

Isolate $x^2$ by subtracting $64$ from both sides:

Take the square root of both sides. Since a side length must be positive, use the positive root:

This gives $x = 15$, so the other leg of the triangle is 15, which corresponds to choice C.