bharat bajaj
Last Activity: 10 Years ago
Both the points lie on the equator, so forget about the earth. Think of just a equatorial circle.
a) Say A is Quito and B is Kampala.
Angle subtended by A at the centre of circle = - 82 degrees 30 minutes.
Angle subtended by B at the centre of circle = + 37 degrees 30 minutes
Total angle subtended at centre = 120 degrees
Hence, shortest path would be along the equator = Length of arc = 120/360 x Circumference = 2.pi.r/3
b) Direct path would be the line joing the two points. We have to find the length of the chord which subtends 120 degrees at the centre.
Make a line from centre to chord. Say this point is D on AB. It is the midpoint. So, DB subtends 60 degrees at the centre.
DB = r sin 60
Length of chord = 2r sin 60
Thanks
Bharat Bajaj
IIT Delhi
askiitians faculty
