To solve for the missing side $x$ of the right triangle, we will use the Pythagorean Theorem, which states:

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

• $c$ is the hypotenuse (the longest side of the right triangle),
• $a$ and $b$ are the two legs (shorter sides).

From the image:

• Hypotenuse $c = 6$
• One leg $a = 2.5$
• Missing side $x = b$

Step-by-Step Solution:

1. Plug values into the Pythagorean Theorem: $a^2 + b^2 = c^2$ $(2.5)^2 + x^2 = 6^2$

2. Square the known values: $(2.5)^2 = 6.25 \quad \text{and} \quad 6^2 = 36$ So: $6.25 + x^2 = 36$

3. Solve for $x^2$: $x^2 = 36 - 6.25$ $x^2 = 29.75$

4. Take the square root of both sides: $x = \sqrt{29.75}$

5. Simplify: $x \approx 5.45$

Final Answer:

The missing side $x$ is approximately 5.45 units.

Do you need further clarification or a deeper explanation? Let me know!

Here are 5 related questions to extend your learning:

1. How do you recognize the hypotenuse in a right triangle?
2. Can the Pythagorean Theorem be used in non-right triangles?
3. If all three sides of a triangle are integers, what is that called (e.g., 3-4-5)?
4. How would you solve for a missing leg if the hypotenuse and other leg were given?
5. Can you derive the Pythagorean Theorem from geometric principles?

Tip: Always square each term in the Pythagorean Theorem carefully to avoid errors!