In a right triangle, $a$ and $b$ are the lengths of the legs, and $c$ is the length of the hypotenuse. Given that $a = 7$ meters and $c = 8$ meters, we need to find the length of $b$, rounded to the nearest tenth.

1. Problem Description

In a right triangle, $a$ and $b$ are the lengths of the legs, and $c$ is the length of the hypotenuse. Given that $a = 7$ meters and $c = 8$ meters, we need to find the length of $b$, rounded to the nearest tenth.

2. Solution Steps

We can use the Pythagorean theorem to find the missing leg length. The Pythagorean theorem states:

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

where $a$ and $b$ are the lengths of the legs and $c$ is the length of the hypotenuse.

We are given $a=7$ and $c=8$. Substituting these values into the formula:

$7^2 + b^2 = 8^2$

$49 + b^2 = 64$

Subtract 49 from both sides:

$b^2 = 64 - 49$

$b^2 = 15$

Take the square root of both sides:

$b = \sqrt{15}$

$b \approx 3.87298$

Rounding to the nearest tenth, we get $b \approx 3.9$.

3. Final Answer

3. 9 meters