We are given a right triangle with legs $a$ and $b$, and hypotenuse $c$. We are given the values of $b$ and $c$, $b = 80$ yards and $c = 100$ yards. We need to find the length of leg $a$. We should round to the nearest tenth if necessary.

1. Problem Description

We are given a right triangle with legs $a$ and $b$, and hypotenuse $c$. We are given the values of $b$ and $c$, $b = 80$ yards and $c = 100$ yards. We need to find the length of leg $a$. We should round to the nearest tenth if necessary.

2. Solution Steps

We can use the Pythagorean theorem to solve for $a$. The Pythagorean theorem states:

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

We are given $b = 80$ and $c = 100$. Substitute these values into the equation:

$a^2 + 80^2 = 100^2$

$a^2 + 6400 = 10000$

Subtract 6400 from both sides:

$a^2 = 10000 - 6400$

$a^2 = 3600$

Take the square root of both sides:

$a = \sqrt{3600}$

$a = 60$

3. Final Answer

The length of leg $a$ is 60 yards.

Final Answer: 60