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Question Number 10227 by Tawakalitu ayo mi last updated on 30/Jan/17

An aeroplane leaves a port P(51°S,  29°E) and  after flying 7597 km due north it reached   another port R. calculate the.  (i) Latitude of R correct to the nearest degree  (ii) Radius of parallel of latitude through R  to the nearest whole number.

$$\mathrm{An}\:\mathrm{aeroplane}\:\mathrm{leaves}\:\mathrm{a}\:\mathrm{port}\:\mathrm{P}\left(\mathrm{51}°\mathrm{S},\:\:\mathrm{29}°\mathrm{E}\right)\:\mathrm{and} \\ $$$$\mathrm{after}\:\mathrm{flying}\:\mathrm{7597}\:\mathrm{km}\:\mathrm{due}\:\mathrm{north}\:\mathrm{it}\:\mathrm{reached}\: \\ $$$$\mathrm{another}\:\mathrm{port}\:\mathrm{R}.\:\mathrm{calculate}\:\mathrm{the}. \\ $$$$\left(\mathrm{i}\right)\:\mathrm{Latitude}\:\mathrm{of}\:\mathrm{R}\:\mathrm{correct}\:\mathrm{to}\:\mathrm{the}\:\mathrm{nearest}\:\mathrm{degree} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{Radius}\:\mathrm{of}\:\mathrm{parallel}\:\mathrm{of}\:\mathrm{latitude}\:\mathrm{through}\:\mathrm{R} \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{nearest}\:\mathrm{whole}\:\mathrm{number}. \\ $$

Answered by mrW1 last updated on 30/Jan/17

Radius of Earth = 6371 km  (i)  ((7597)/(2π×6371))×360≈68°  51°−68°=−17°  ⇒Latitude of R: 17°N  (ii)  6371×cos 17°≈6093 km

$${Radius}\:{of}\:{Earth}\:=\:\mathrm{6371}\:{km} \\ $$$$\left({i}\right) \\ $$$$\frac{\mathrm{7597}}{\mathrm{2}\pi×\mathrm{6371}}×\mathrm{360}\approx\mathrm{68}° \\ $$$$\mathrm{51}°−\mathrm{68}°=−\mathrm{17}° \\ $$$$\Rightarrow{Latitude}\:{of}\:{R}:\:\mathrm{17}°{N} \\ $$$$\left({ii}\right) \\ $$$$\mathrm{6371}×\mathrm{cos}\:\mathrm{17}°\approx\mathrm{6093}\:{km} \\ $$

Commented by Tawakalitu ayo mi last updated on 30/Jan/17

God bless you sir.

$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$

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