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An aeroplane flies from point A #(1^0 15'S, 37^0E)# to a point B directly North of A. The arc AB subtends an angle of #45^0# at the centre of the earth. From B, the aeroplane flies due west to point C on longitude #23^0W#. (Take the value of #pi \ as 22/7# and radius of the earth as 6370km)
(a) (i) Find the latitude of B (ii) Find the distance travelled by the aeroplane between B and C
(b) The aeroplane left B at 1.00 am local time. When the aeroplane was leaving B, what was the local time at C?