The problem states that in a right triangle, $a$ and $b$ are the lengths of the legs, and $c$ is the length of the hypotenuse. We are given $b = 6$ yards and $c = 9$ yards. We need to find the length of side $a$ and round to the nearest tenth if necessary.

1. Problem Description

The problem states that in a right triangle, $a$ and $b$ are the lengths of the legs, and $c$ is the length of the hypotenuse. We are given $b = 6$ yards and $c = 9$ yards. We need to find the length of side $a$ and round to the nearest tenth if necessary.

2. Solution Steps

We can use the Pythagorean theorem to solve for the missing side $a$. The Pythagorean theorem states that

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

We are given $b=6$ and $c=9$. Substituting these values into the equation, we have

$a^2 + 6^2 = 9^2$

$a^2 + 36 = 81$

Subtract 36 from both sides:

$a^2 = 81 - 36$

$a^2 = 45$

Take the square root of both sides:

$a = \sqrt{45}$

$a \approx 6.7082$

Round to the nearest tenth:

$a \approx 6.7$

3. Final Answer

$a = 6.7$ yards