How many triangles ABC, no two of them congruent, can be drawn with AB = 7 cm, BC = 5 cm and ∠A = 30°?

The data is two sides and a non-included angle, the ambiguous SSA case. Draw ∠A = 30° and mark B on one arm with AB = 7 cm. The perpendicular distance from B to the other arm is 7 × sin 30° = 3.5 cm. An arc of radius BC = 5 cm centred at B therefore cuts that arm twice, since 3.5 < 5 < 7, giving exactly two non-congruent triangles — one with an acute angle at C and one with an obtuse angle at C. Had BC been under 3.5 cm there would be none, and had BC been 7 cm or more there would be exactly one. This is precisely why SSA is not a congruence criterion.