The image shows a right triangle where one leg is 5, another leg is 8, and you are asked to find the hypotenuse $x$.

We can use the Pythagorean theorem to solve this, which states that in a right triangle:

$x^2 = a^2 + b^2$

Where:

• $x$ is the hypotenuse (the side opposite the right angle, which we need to find),
• $a = 5$ and $b = 8$ are the two legs of the triangle.

Let's calculate $x$:

$x^2 = 5^2 + 8^2 = 25 + 64 = 89$

Now, take the square root of both sides to find $x$:

$x = \sqrt{89} \approx 9.43$

So, the value of $x$ is approximately 9.43.

Would you like a more detailed breakdown of the steps?

Here are some related questions to explore:

1. What are the conditions for using the Pythagorean theorem?
2. Can the Pythagorean theorem be applied to non-right triangles?
3. How can we verify the accuracy of the square root calculation for $x$?
4. What are some real-life applications of the Pythagorean theorem?
5. How would the solution change if the triangle were scaled?

Tip: When working with right triangles, the Pythagorean theorem is a powerful tool to solve for missing sides as long as the triangle has a right angle.