Final answer:
The conditions of angles 27° and 39° with an included side of 17 cm meet the side-angle-side (SAS) condition, which guarantees the formation of one unique triangle.
Step-by-step explanation:
The student has asked whether the given conditions (angles of 27° and 39° with an included side of 17 cm) determine one unique triangle, multiple similar triangles, multiple nonidentical triangles, or no triangle at all. To answer this, we need to recall that the sum of the angles in any triangle must be 180 degrees. Given two angles, the third angle can be determined by subtracting the sum of the two given angles from 180 degrees. In this case:
3rd angle = 180° - (27° + 39°) = 180° - 66° = 114°
With all three angles known, and the length of the side included between the two angles given, this will lead to a unique triangle. This is because the side-angle-side (SAS) condition is met, which is one of the congruence conditions that guarantees one unique triangle can be formed.