The problem states that we have a right triangle with legs $a$ and $b$, and hypotenuse $c$. We are given that $a = 63$ yards and $c = 87$ yards. We need to find the length of leg $b$, rounding to the nearest tenth if necessary.

1. Problem Description

The problem states that we have a right triangle with legs $a$ and $b$, and hypotenuse $c$. We are given that $a = 63$ yards and $c = 87$ yards. We need to find the length of leg $b$, rounding to the nearest tenth if necessary.

2. Solution Steps

We will use the Pythagorean theorem, which states:

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

We are given $a=63$ and $c=87$. We need to find $b$. Substituting the given values into the Pythagorean theorem:

$63^2 + b^2 = 87^2$

$3969 + b^2 = 7569$

Subtract 3969 from both sides:

$b^2 = 7569 - 3969$

$b^2 = 3600$

Take the square root of both sides:

$b = \sqrt{3600}$

$b = 60$

3. Final Answer

The value of $b$ is 60.0 yards.