To find the length of $b$ in this right triangle, we can use the Pythagorean theorem again:

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

Given:

• $a = 3$ mm
• $c = 6$ mm

We want to solve for $b$. So, rearrange the equation:

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

Now, substitute the values of $a$ and $c$:

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

Now, take the square root of both sides to find $b$:

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

So, the length of $b$ is approximately 5.2 mm when rounded to the nearest tenth.

Let me know if you need any more clarification or further calculations!

Here are some related questions:

1. What are other ways to solve for unknown sides in right triangles besides using the Pythagorean theorem?
2. How do you calculate the angles of a right triangle if you know