Given that a, b, and c, the sides of a triangle, are such that a^2, b^2, and c^2, form an arithmetic sequence, show that cot A, cot B, and cot C also form an arithmetic sequence.

An airplane is flying at an elevation of 5150 ft, directly above a straight highway. two motorists are driving cars on the highway on opposite sides of the plane, and the angle of depression to one car is 35 ̊ and to the other is 52 ̊. how far apart are the cars?