(a) Firstly, wherever point C is located, angle A and angle B of triangle ABC must both be acute angles. Hence, angle C must be obtuse for triangle ABC to be an obtuse triangle. Secondly, the probability of point C being inside a region where angle C is obtuse is the ratio of the area of that region to the area of the square. Since the area of the square is one, the probability of C lying in a particular region is the...