Two towns K and Q are on the parallel of latitude 46^\circN. The longitude of town K is 130^\circW and that of town Q is 103^\circW. A third town P also on latitude 46^\circN is on longitude 23^\circE, Calculate:
(i) the length of the parallel of latitude 46^\circN, 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]
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(i)
The length of the parallel of latitude 46^\circN = \(2 \pi R \cos 46^\circ\)
= \(2 \times 3.142 \times 6400 \times 0.6947\)
= \(27,939.167 km \approxeq 28000 km\) (to the nearest 100km)
(ii)
Longitudinal difference between K and Q = 130^\circ - 103^\circ = 27^\circ
Distance between K and Q = length of arc KQ
= \(\frac{27}{360} \times 2 \times 3.142 \times 6400 \times \cos 46^\circ\)
= \(2,095.31 km \approxeq 2100km\) (to the nearest 100km)
(iii)
Longitudinal difference between Q and P = 103^\circ + 23^\circ = 126^\circ
Distance between Q and P = \(\frac{126}{360} \times 2 \times 3.142 \times 6400 \times \cos 46^\circ\)
= \(9778.12 km \approxeq 9780 km\) (to the nearest 10km)
Source: Myschool Past Questions Archive (Record #54716)