The diagram represents a right triangle with the following dimensions:

• The hypotenuse is labeled $9$,
• One leg is labeled $4.5$,
• The other leg is labeled $x$ (to be determined).

We can solve for $x$ using the Pythagorean Theorem:

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

Where:

• $a$ and $b$ are the legs of the triangle,
• $c$ is the hypotenuse.

Substituting the values:

$4.5^2 + x^2 = 9^2$

Step 1: Calculate $4.5^2$ and $9^2$:

$4.5^2 = 20.25, \quad 9^2 = 81$

Step 2: Substitute into the equation:

$20.25 + x^2 = 81$

Step 3: Solve for $x^2$:

$x^2 = 81 - 20.25 = 60.75$

Step 4: Solve for $x$ (take the square root):

$x = \sqrt{60.75} \approx 7.8$

Final Answer:

$x \approx 7.8$

Would you like a step-by-step breakdown or clarification of any part?

Related Questions:

1. How does the Pythagorean Theorem apply to real-world problems?
2. Can this triangle's angles be calculated using trigonometry?
3. How do you approximate square roots by hand?
4. What is the significance of right triangles in geometry?
5. How would the result change if the hypotenuse was different?

Tip:

When solving for missing sides in a right triangle, always double-check your square root calculation for accuracy!