Question 809507: Entebbe, Uganda and Sasak, Sumatra, are on the equator. Sasak is 4700 mi east of Entebee (longitude 32.5 E). Find the longitude of Sasak.
Please walk me through the steps to get an answer.
I'm more concerned with the process than the result.
Thank you.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! You need some information about Earth's dimensions, which may have been given in class or in your textbook. If you were given some number, it would be wise to use
the number given.
What I found online is as follows:
Earth's circumference at the equator is 24,900 miles.
Earth's diameter is 7,900 miles (12,760 km) at the equator.
Earth's radius is 3,950 miles (6,380 km) at the equator.
The circumference of Earth at the equator is divided into  to determine longitude.
By definition, all places along the shortest curve from a point in the equator to a pole have the same longitude.
The  for longitude was arbitrarily set at the Greenwich observatory in England, and longitude is measured East and West from there.
If you were given the radius, or the diameter you can find the circumference as
 or  .
The difference in longitude between two places on the equator,  can be found from the angle and distance proportion
With the information I found, the difference in longitude between Sasak and Entebbe is given by
So Sasak is  (rounding) east of Entebbe,
and its longitude must be
   
Since that is less than  , it counts as longitude  .
If it had been more than , we would have to calculate the smaller angle to longitude zero, and it would be W instead of E.
For example,  east of longitude zero, is really west of longitude zero, or 178W.
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