Question Number 10227 by Tawakalitu ayo mi last updated on 30/Jan/17
$$\mathrm{An}\:\mathrm{aeroplane}\:\mathrm{leaves}\:\mathrm{a}\:\mathrm{port}\:\mathrm{P}\left(\mathrm{51}°\mathrm{S},\:\:\mathrm{29}°\mathrm{E}\right)\:\mathrm{and} \\ $$$$\mathrm{after}\:\mathrm{flying}\:\mathrm{7597}\:\mathrm{km}\:\mathrm{due}\:\mathrm{north}\:\mathrm{it}\:\mathrm{reached}\: \\ $$$$\mathrm{another}\:\mathrm{port}\:\mathrm{R}.\:\mathrm{calculate}\:\mathrm{the}. \\ $$$$\left(\mathrm{i}\right)\:\mathrm{Latitude}\:\mathrm{of}\:\mathrm{R}\:\mathrm{correct}\:\mathrm{to}\:\mathrm{the}\:\mathrm{nearest}\:\mathrm{degree} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{Radius}\:\mathrm{of}\:\mathrm{parallel}\:\mathrm{of}\:\mathrm{latitude}\:\mathrm{through}\:\mathrm{R} \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{nearest}\:\mathrm{whole}\:\mathrm{number}. \\ $$
Answered by mrW1 last updated on 30/Jan/17
$${Radius}\:{of}\:{Earth}\:=\:\mathrm{6371}\:{km} \\ $$$$\left({i}\right) \\ $$$$\frac{\mathrm{7597}}{\mathrm{2}\pi×\mathrm{6371}}×\mathrm{360}\approx\mathrm{68}° \\ $$$$\mathrm{51}°−\mathrm{68}°=−\mathrm{17}° \\ $$$$\Rightarrow{Latitude}\:{of}\:{R}:\:\mathrm{17}°{N} \\ $$$$\left({ii}\right) \\ $$$$\mathrm{6371}×\mathrm{cos}\:\mathrm{17}°\approx\mathrm{6093}\:{km} \\ $$
Commented by Tawakalitu ayo mi last updated on 30/Jan/17
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$