How many miles between a point 60 ° north latitude and 30 ° west longitude and a point 60 ° north latitude and 60 ° east longitude?

-- We're pretty sure that this question is based on an assumption of EARTH, so we know that we're dealing with a sphere of roughly 3.950 miles radius.

-- The distance on the sphere between 30° west and 60° east is 90° of longitude.  That's 1/4 of the total circumference of the circle.  

-- BUT Way up here at 60° N latitude, the circle is not as big as the equator.  It's radius/diameter/circumference is only cos(60°) = 0.5 of the Earth's total.

-- So the length of our quarter-circle arc is about

(1/4) x (2 · π · 3,950 miles) x (0.5) =

(1/4) x (3,950 π miles) =

988 π miles = 3,104 miles