Two towns K and Q are on the parallel of latitude 46°N. The longitude of town K is 130°W and that of town Q is 103°W. A third town P also on latitude 46°N is on longitude 23°E, Calculate:
(i) the length of the parallel of latitude 46°N, to the nearest 100km;
(ii) the distance between K and Q, correct to the nearest 100km;
(iii) the distance between Q and P measured along the parallel of latitude, to the nearest 10km.
[Take (pi = 3.142); Radius of the earth = 6400km]
Explanation
(i)
The length of the parallel of latitude 46°N = (2 pi R cos 46°)
= (2 times 3.142 times 6400 times 0.6947)
= (27,939.167 km approxeq 28000 km) (to the nearest 100km)
(ii)
Longitudinal difference between K and Q = 130° – 103° = 27°
Distance between K and Q = length of arc KQ
= (frac{27}{360} times 2 times 3.142 times 6400 times cos 46°)
= (2,095.31 km approxeq 2100km) (to the nearest 100km)
(iii)
Longitudinal difference between Q and P = 103° + 23° = 126°
Distance between Q and P = (frac{126}{360} times 2 times 3.142 times 6400 times cos 46°)
= (9778.12 km approxeq 9780 km) (to the nearest 10km)