Across smallest side- smallest angle.
across largest side- largest angle
largest side is AC, so largest angle is B
smallest side is AB, so smallest angle is C
angles from smallest to largest : C, A, B
The confidence interval would be

.
We use the formula

, where

, with p being the sample proportion and N being the sample size.
First we find the z-score associated with this level of confidence:
Convert 95% to a decimal: 95/100 = 0.95
Subtract from 1: 1-0.95 = 0.05
Divide by 2: 0.05/2 = 0.025
Subtract from 1: 1-0.025 = 0.975
Using a z-table (http://www.z-table.com) we see that this value is associated with a z-score of 1.96.
Since 578/720 said yes, this gives us p=0.80:

This gives us
This is applying the formula

We have a slight problem, though, because we are measuring rate in miles per hour, and we are measuring time in minutes. To make this problem solvable, we need to convert to either miles per minute or convert the time to hours. I'm going to convert the 15 minutes into hours:

Now that all of the units match, we have:

You can finish from there I'm sure.