Transitional engineering students are those who are academically ineligible to enter a bachelor's engineering program but are enrolled in an associate engineering program with a university. Successful completion of such an associate engineering program allows the higher achievers to transfer to a full bachelor's engineering program. The associate engineering program is taken commonly by self-employed tradesmen, technical workers, and young apprentices in regional, rural, and remote (RRR) areas. The foundation engineering mathematics course in the associate engineering program, particularly knowledge and skills in solving word problems involving triangles, plays a key role for the smooth transition of these students to the engineering disciplinary courses. However, there is little we have known about the performances of the transitional engineering students in solving problems involving triangles as the associate engineering programs are not among the mainstream of undergraduate programs. This study analyzed the 27 transitional engineering students' performances in solving word problems involving triangles assigned to the students in the foundation mathematics course at a regional Australian university and found that the RRR transitional engineering students demonstrated a higher level of study ethics and achievement in solving word problems involving triangles, compared with the RRR student mathematics teachers. This seems mainly due to the professional experiences in delivering real-world projects prior to the start of their mathematics learning. Further research should be expanded to more areas of mathematics to gauge the overall performances of the transitional engineering students in mathematics learning and progression.