A boat sails for 5 hours at 30 mph in a direction 164°56'. How far south has it sailed (to the nearest mile) ?

Total distance covered = 5 x 30 = 150 miles

Angle of travel with respect to south pole = 180 - 164°56' = 15°4'

Let the distance southwards covered be x, then

cos 15°4' = x/150

Thus, x = 150 cos 15°4' = 144.84

Therefore, the distance covered southwards = 145 miles to the nearest mile.