In a right triangle, the lengths of the legs are $a$ and $b$, and the length of the hypotenuse is $c$. Given that $a = 2$ inches and $c = 6$ inches, we need to find the length of leg $b$. We are asked to round the answer to the nearest tenth if necessary.

1. Problem Description

In a right triangle, the lengths of the legs are $a$ and $b$, and the length of the hypotenuse is $c$. Given that $a = 2$ inches and $c = 6$ inches, we need to find the length of leg $b$. We are asked to round the answer to the nearest tenth if necessary.

2. Solution Steps

We will use the Pythagorean theorem to solve for $b$. The Pythagorean theorem states that for a right triangle with legs of length $a$ and $b$, and a hypotenuse of length $c$, the following equation holds:

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

We are given that $a = 2$ and $c = 6$. Substituting these values into the equation, we get:

$2^2 + b^2 = 6^2$

$4 + b^2 = 36$

Subtract 4 from both sides of the equation to isolate $b^2$:

$b^2 = 36 - 4$

$b^2 = 32$

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

$b = \sqrt{32}$

We can simplify $\sqrt{32}$ as $\sqrt{16 \cdot 2} = \sqrt{16} \cdot \sqrt{2} = 4\sqrt{2}$.

To find the value to the nearest tenth, we can calculate:

$b = \sqrt{32} \approx 5.656854...$

Rounding to the nearest tenth, we get $b \approx 5.7$.

3. Final Answer

$b = 5.7$ inches