In a right triangle, the lengths of the legs are $a$ and $b$, and the length of the hypotenuse is $c$. Given that $a = 57$ meters and $c = 95$ meters, we need to find the value of $b$, rounded to the nearest tenth.

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 $a = 57$ meters and $c = 95$ meters, we need to find the value of $b$, rounded to the nearest tenth.

2. Solution Steps

We use the Pythagorean theorem to find $b$:

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

We are given $a = 57$ and $c = 95$. Substitute these values into the Pythagorean theorem:

$57^2 + b^2 = 95^2$

$3249 + b^2 = 9025$

Subtract $3249$ from both sides:

$b^2 = 9025 - 3249$

$b^2 = 5776$

Take the square root of both sides:

$b = \sqrt{5776}$

$b = 76$

3. Final Answer

$b = 76.0$ meters