To solve for $x$ in the given right triangle, we can apply the Pythagorean Theorem. The theorem states that for any 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 diagram, $x$ is the hypotenuse, and the other two sides are given as 8 and 15. So, we have:

$x^2 = 8^2 + 15^2$

Let's calculate:

$x^2 = 64 + 225 = 289$

Taking the square root of both sides:

$x = \sqrt{289} = 17$

Thus, the length of side $x$ is $17$.

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:

1. What is the Pythagorean theorem, and why does it apply to right triangles?
2. How do you identify the hypotenuse in a right triangle?
3. Can the Pythagorean theorem be used for non-right triangles?
4. What are the steps to solve for a missing leg in a right triangle, given the hypotenuse and one side?
5. How would you solve this problem if the triangle's sides were given in decimals instead of whole numbers?

Tip: In any right triangle, the hypotenuse is always the side opposite the right angle and is the longest side.