I need to Find the distance between the cities. Assume that Earth is a sphere of radius 4000 miles ?
The cities are
Johannesburg, South Africa 26° 8' S
Jerusalem, Israel 31° 46' N
- ElmyrLv 71 decade agoFavorite Answer
You need to know the longitude too.
Lat1 = first latitude in radians
Lon1 = first longitude in radians
Lat2 = second latitude in radians
Lon2 = second longitude in radians
r = radius
d = distance (same unit as radius)
Convert degrees to decimal:
decimal = D + M/60 + S/3600
Convert degrees to radians
radians = degrees * π/180°
Spherical law of cosines:
d = r * arccos[sin Lat1 * sin Lat2 + cos Lat1 * cos Lat2 * cos (Lon2 - Lon1)]
d = 4000 * arccos[sin -26.204444π/180 * sin 31.783333π/180 + cos -26.204444π/180 * cos 31.783333π/180 * cos (35.216667π/180 - 28.045556π/180)]
d = 8105.015755 miles
d ≈ 8105 miles
- Anonymous4 years ago
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- 5 years ago
Trip #1: d = rt Trip #2: D = RT t + T = 4.4 r = 50 mph R = 60 mph d = D => rt = RT => r(4.4 - T) = RT => 4.4r = RT + rT => T = ( 4.4r ) / (R + r) put in the numbers T = 4.4*50 / 110 T = 2 [hrs] Therefore D = RT = 60*2 = 120 [mi] and d = rt = 50*(4.4 - 2) = 120 [mi] The distance is 120 miles.