The problem asks to find the length of the missing leg $b$ in a right triangle, given the lengths of the other leg (3 cm) and the hypotenuse (7 cm). We need to use the Pythagorean theorem to find the value of $b$.

1. Problem Description

The problem asks to find the length of the missing leg $b$ in a right triangle, given the lengths of the other leg (3 cm) and the hypotenuse (7 cm). We need to use the Pythagorean theorem to find the value of $b$.

2. Solution Steps

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse ($c$) is equal to the sum of the squares of the lengths of the other two sides ($a$ and $b$). The formula is:

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

In this problem, we have $a = 3$ cm, $c = 7$ cm, and we want to find $b$. Plugging in the known values into the Pythagorean theorem, we have:

$3^2 + b^2 = 7^2$

$9 + b^2 = 49$

To solve for $b^2$, we subtract 9 from both sides:

$b^2 = 49 - 9$

$b^2 = 40$

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

$b = \sqrt{40}$

We can simplify $\sqrt{40}$ as $\sqrt{4 \times 10} = 2\sqrt{10}$. To round to the nearest tenth, we need to approximate the value of $\sqrt{40}$.

Since $6^2 = 36$ and $7^2 = 49$, $\sqrt{40}$ is between 6 and

7. Using a calculator, $\sqrt{40} \approx 6.32455532$.

Rounding to the nearest tenth, we get $b \approx 6.3$.

3. Final Answer

$b = 6.3$ centimeters