To find the length of the missing leg ($a$) of the right triangle in the image, we can use the Pythagorean Theorem:

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

Where:

• $c$ is the hypotenuse ($15 \, \text{m}$),
• $b$ is the given leg ($9 \, \text{m}$),
• $a$ is the missing leg.

Steps:

1. Substitute the known values into the formula: $15^2 = a^2 + 9^2$

2. Simplify the squares: $225 = a^2 + 81$

3. Solve for $a^2$: $a^2 = 225 - 81$ $a^2 = 144$

4. Take the square root of both sides: $a = \sqrt{144}$ $a = 12 \, \text{m}$

Final Answer:

The length of the missing leg ($a$) is 12 meters.

Would you like more details or help with any other aspect?

Here are 5 related questions to explore further:

1. What is the general form of the Pythagorean Theorem?
2. How can the Pythagorean Theorem be applied in 3D geometry?
3. What are the properties of right triangles?
4. How do you calculate the hypotenuse if both legs are known?
5. Can the Pythagorean Theorem be used to find distances in coordinate geometry?

Tip: Always double-check your calculations, especially when squaring and taking square roots!