# Math Help - Great Circles.

1. ## Great Circles.

Great Circles!

Use the points:

C
( 40 N , 70 W )
D ( 40 N , 150 W )E( 70 N , 150 W ) F ( 70 N , 70 W )

to find the distance from C to E along a great circle.

( Hint: You will need to find the lengths of the Trapezium CDEF)

Any Contribution and Help will be Appreciated.

Thanks!!!

2. Originally Posted by Pandp77
Great Circles![LEFT]
Use the points:

C
( 40 N , 70 W )
D ( 40 N , 150 W )E( 70 N , 150 W ) F ( 70 N , 70 W )

[COLOR=Blue][SIZE=5][FONT=Trebuchet MS]to find the distance from C to E along a great circle.

[I][COLOR=Black]( Hint: You will need to find the lengths of the Trapezium CDEF)

Any Contribution and Help will be Appreciated.

Thanks!!!
Let P denote the north pole then you can use the triangle CPE to calculate the distance CE. Use the Cosine rule of a spheric triangle: (d is the angle corresponding to the distance between C and E)

$\cos(d)=\sin(70^\circ) \sin(150^\circ) + \cos(70^\circ) \cos(150^\circ) \cos(70^\circ - 40^\circ)\approx 0.21333...$

which will yield $d \approx 77.68^\circ$