The distance traveled along the great circle (shortest distance on a sphere) in kilometers is given by
d = (x / 360°) * 40,000 km
where x is the angle from the center of the earth (central angle) that the track sweeps as it crosses the country.
It turns out, x also appears in the following trigonometric equation, in which the only unknown to you now is the angle x!
cos(x) = sin(Lat1) * sin(Lat2) + cos(Lat1) * cos(Lat2) * cos(Long1 - Long2)
Figure out the distance traveled across the USA by the eclipse by the following steps, working them out on the back of this sheet:
Find the Latitude and Longitude of both cities as degrees in decimals to the nearest thousandth using the conversions and example above.
Throw those Latitudes and Longitudes in decimal degrees into the right side of the cosine x formula, and use an inverse cosine to find x in degrees. It's the only unknown!
Finally, put x in the distance formula above to determine the length in kilometers of the eclipse track across the USA! How would you check?