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The-position-of-a-point-A-is-41-N-18-E-point-B-is-8000-km-due-west-of-A-Find-the-longitude-of-B-to-the-nearest-degree-




Question Number 9203 by tawakalitu last updated on 23/Nov/16
The position of a point A is (41°N, 18°E)  point B is 8000 km due west of A. Find the  longitude of B to the nearest degree.
$$\mathrm{The}\:\mathrm{position}\:\mathrm{of}\:\mathrm{a}\:\mathrm{point}\:\mathrm{A}\:\mathrm{is}\:\left(\mathrm{41}°\mathrm{N},\:\mathrm{18}°\mathrm{E}\right) \\ $$$$\mathrm{point}\:\mathrm{B}\:\mathrm{is}\:\mathrm{8000}\:\mathrm{km}\:\mathrm{due}\:\mathrm{west}\:\mathrm{of}\:\mathrm{A}.\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{longitude}\:\mathrm{of}\:\mathrm{B}\:\mathrm{to}\:\mathrm{the}\:\mathrm{nearest}\:\mathrm{degree}. \\ $$
Answered by mrW last updated on 23/Nov/16
The radius of the Earth is roughly  R=6371 km.  r=6371×cos 41°=4808 km  ((8000)/(2π×4808))×360≈95°  18−95=−77  The langitude of point B is 77°W.
$$\mathrm{The}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{the}\:\mathrm{Earth}\:\mathrm{is}\:\mathrm{roughly} \\ $$$$\mathrm{R}=\mathrm{6371}\:\mathrm{km}. \\ $$$$\mathrm{r}=\mathrm{6371}×\mathrm{cos}\:\mathrm{41}°=\mathrm{4808}\:\mathrm{km} \\ $$$$\frac{\mathrm{8000}}{\mathrm{2}\pi×\mathrm{4808}}×\mathrm{360}\approx\mathrm{95}° \\ $$$$\mathrm{18}−\mathrm{95}=−\mathrm{77} \\ $$$$\mathrm{The}\:\mathrm{langitude}\:\mathrm{of}\:\mathrm{point}\:\mathrm{B}\:\mathrm{is}\:\mathrm{77}°\mathrm{W}.\: \\ $$
Commented by tawakalitu last updated on 23/Nov/16
Thank you sir. God bless you.
$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{sir}.\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}. \\ $$

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