We are given a right triangle with legs $a$ and $b$, and hypotenuse $c$. We are given that $a=2$ yards and $c=3$ yards. We need to find the length of leg $b$. We need to 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 that $a=2$ yards and $c=3$ yards. We need to find the length of leg $b$. We need to round to the nearest tenth if necessary.

2. Solution Steps

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. The formula is:

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

We are given $a = 2$ and $c = 3$. We want to find $b$. Substitute the given values into the formula:

$2^2 + b^2 = 3^2$

$4 + b^2 = 9$

Subtract 4 from both sides of the equation:

$b^2 = 9 - 4$

$b^2 = 5$

Take the square root of both sides:

$b = \sqrt{5}$

Now we approximate the square root of 5 to the nearest tenth:

$\sqrt{5} \approx 2.236$

Rounding to the nearest tenth, we get $b \approx 2.2$.

3. Final Answer

2.2 yards