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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.

For the following right triangle, find the side length x, where the other two sides are 8 and 15.

Learn how to find the hypotenuse in a right triangle where the given sides are 8 and 15. This example demonstrates the use of the Pythagorean theorem, perfect for students in Grades 8-10.

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