This problem involves finding the unknown side length $x$ of a right triangle using the Pythagorean Theorem, which states:

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

Here:

• $a = x$ (the unknown side we are solving for),
• $b = 9$ (the other leg of the triangle),
• $c = 40$ (the hypotenuse, since it is the longest side).

Steps to Solve:

1. Plug the known values into the Pythagorean Theorem: $x^2 + 9^2 = 40^2$

2. Simplify the squares: $x^2 + 81 = 1600$

3. Subtract 81 from both sides: $x^2 = 1600 - 81$ $x^2 = 1519$

4. Take the square root of both sides to solve for $x$: $x = \sqrt{1519}$

5. Approximate the square root (if needed): $x \approx 38.97$

Final Answer:

$x \approx 38.97$

Would you like more details or additional clarification?

5 Related Questions:

1. How do you determine which side is the hypotenuse in a right triangle?
2. What are the practical applications of the Pythagorean Theorem?
3. How can you solve a right triangle problem if all sides are integers (a Pythagorean triple)?
4. What is the geometric meaning of squaring the sides of a triangle?
5. How do you find the area of a right triangle once all side lengths are known?

Tip:

Always double-check which side is the hypotenuse (the longest side) before applying the Pythagorean Theorem.