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 i...

Answer Details

Radius \(R=6400\) km, \(\pi=3.142\), latitude \(46^{\circ}\N\), \(\cos46^{\circ}=0.6947\).

(i) Length of the parallel of latitude \(46^{\circ}\)N

\[L=2\pi R\cos46^{\circ}=2(3.142)(6400)(0.6947)=27{,}940\text{ km}\approx\mathbf{27{,}900\text{ km}}\ (\text{nearest }100).\]

(ii) Distance K to Q (same latitude). \(K\) at \(130^{\circ}\W\), \(Q\) at \(103^{\circ}\W\): difference \(=27^{\circ}\).

\[d_{KQ}=\frac{27}{360}\times27{,}940=2095\text{ km}\approx\mathbf{2100\text{ km}}\ (\text{nearest }100).\]

(iii) Distance Q to P along the parallel. \(Q\) at \(103^{\circ}\W\), \(P\) at \(23^{\circ}\E\): difference \(=103^{\circ}+23^{\circ}=126^{\circ}\).

\[d_{QP}=\frac{126}{360}\times27{,}940=9779\text{ km}\approx\mathbf{9780\text{ km}}\ (\text{nearest }10).\]