The Position of two A and B on the earth’s surface are (36°N, 49°E) and (360°N, 131°W ) respectively.
(a) The difference in long between town A and town
(b) Given that the radius of the earth is 6370, calculate the distance town A and town B.
(c) Another town, C is 840 east of town B and on the same latitude as towns A and B. Find the longitude C.
I assume you meant both points to be at 36°N. They are 180° apart in longitude.
A good discussion on the topic can be found at
http://www.movable-type.co.uk/scripts/gis-faq-5.1.html
or any number of other hits by google.
(a) To find the difference in longitude between town A and town B, subtract the longitude of town A (49°E) from the longitude of town B (131°W).
First, convert the given longitude of town B from degrees West to degrees East. Since 1 degree East is equivalent to 360 degrees West, subtract 131 from 360:
360° - 131° = 229°E
Now subtract the longitude of town A from the converted longitude of town B:
229°E - 49°E = 180°E
Therefore, the difference in longitude between town A and town B is 180°E.
(b) To calculate the distance between town A and town B, we can use the formula for the distance between two points on a sphere (such as the Earth) using their latitude and longitude.
The formula for calculating the distance between two points on a sphere is:
Distance = Radius of Earth x arccos(sin(lat1) x sin(lat2) + cos(lat1) x cos(lat2) x cos(long2 - long1))
First, find the latitude and longitude values for towns A and B:
Town A: Latitude = 36°N, Longitude = 49°E
Town B: Latitude = 36°N, Longitude = 229°E
Convert the latitudes to radians by multiplying them by (π/180):
Lat1 = 36°N x (π/180) = 0.6283 radians
Lat2 = 36°N x (π/180) = 0.6283 radians
Convert the difference in longitudes to radians:
Long2 - Long1 = 180°E x (π/180) = π radians
Now, substitute the values into the formula and calculate the distance:
Distance = 6370 x arccos(sin(0.6283) x sin(0.6283) + cos(0.6283) x cos(0.6283) x cos(π))
Using a calculator, the distance is approximately 8856 km.
Therefore, the distance between town A and town B is approximately 8856 km.
(c) To find the longitude of town C, we know that it is 840 km east of town B and on the same latitude as towns A and B.
Since towns A and B are on the same latitude, the latitude of town C will also be 36°N.
To find the longitude of town C, add the distance of 840 km east to the longitude of town B.
Longitude of town C = Longitude of town B + 840 km
Longitude of town C = 229°E + 840 km
However, since the given longitude of town B is already in degrees East, we don't need to convert it.
Therefore, the longitude of town C is 229°E + 840 km.