Step 1 :The problem provides the time it takes for the pendulum to swing back and forth once, which is 5.72 seconds. It also provides the formula for the time, $t=2 \sqrt{L}$, where $L$ is the length of the pendulum.
Step 2 :We need to find the length of the pendulum, so we rearrange the formula to solve for $L$. We square both sides to get rid of the square root, giving us $t^2 = 4L$.
Step 3 :Then, we divide both sides by 4 to isolate $L$, giving us the formula $L = \frac{t^2}{4}$.
Step 4 :We substitute the given time of 5.72 seconds into this formula to find the length of the pendulum. So, $L = \frac{(5.72)^2}{4}$.
Step 5 :Calculating the above expression, we find that $L = 8.179599999999999$.
Step 6 :Rounding to the nearest tenth, we find that the length of the pendulum is approximately \(\boxed{8.2}\) meters.