We are dealing with a right triangle, and we need to determine the length of the missing leg $b$. The triangle has a hypotenuse of 6 meters and one leg of 3 meters.

We can use the Pythagorean theorem to solve for $b$, which states:

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

Where:

• $a = 3 \, \text{m}$ (one leg),
• $b$ (the unknown leg),
• $c = 6 \, \text{m}$ (the hypotenuse).

Now, we can rearrange the equation to solve for $b$:

$b^2 = c^2 - a^2$

Substitute the known values:

$b^2 = 6^2 - 3^2$ $b^2 = 36 - 9$ $b^2 = 27$

Now, take the square root of both sides:

$b = \sqrt{27} \approx 5.2 \, \text{m}$

Thus, the length of the missing leg $b$ is approximately 5.2 meters.

Would you like more details or have any questions?

Here are some additional related questions:

1. How do we use the Pythagorean theorem for non-right triangles?
2. What are the conditions required to apply the Pythagorean theorem?
3. Can we determine the area of the triangle given the side lengths?
4. How would the answer change if the hypotenuse length were different?
5. How can trigonometric functions be applied to solve for angles in this triangle?

Tip: Always make sure the side opposite the right angle is treated as the hypotenuse when using the Pythagorean theorem.