This is a right triangle with one leg measuring 8 ft, the other leg measuring 9 ft, and the hypotenuse labeled as $x$. To find the hypotenuse $x$, we use the Pythagorean theorem:

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

Where:

• $a = 8$ ft,
• $b = 9$ ft,
• $c = x$ (the hypotenuse).

Substituting the values:

$8^2 + 9^2 = x^2$

$64 + 81 = x^2$

$145 = x^2$

Taking the square root of both sides:

$x = \sqrt{145}$

Approximating $\sqrt{145}$:

$x \approx 12.04 \, \text{ft}.$

Final Answer:

The hypotenuse $x$ is approximately 12.04 ft.

Let me know if you want further details or a breakdown! Here are some related questions to explore:

1. How is the Pythagorean theorem used in different real-life applications?
2. What are the other trigonometric methods to solve a right triangle if angles are known?
3. How can we use a calculator to approximate square roots like $\sqrt{145}$?
4. What is the geometric significance of the hypotenuse in a triangle?
5. Can the same formula be applied in non-right triangles?

Tip: Always check your triangle for a right angle before applying the Pythagorean theorem!