Final answer:
Using the Angle Sum Property, which states that the sum of the angles in a triangle is always 180 degrees, we find that the third angle is 65°. This makes the triangle unique, satisfying the side-angle-side (SAS) condition.
Step-by-step explanation:
Determining a Unique Triangle
To determine if the conditions form a unique triangle, we can use the fact that the sum of the angles in any triangle is 180 degrees. The given angles are 40° and 75°. Adding these gives 115°, which leaves 65° for the third angle (since 180° - 115° = 65°). Thus, there is a unique third angle that forms a unique triangle.
The rule used here is the Angle Sum Property of a triangle, which states that the sum of the interior angles of a triangle is always 180 degrees. With two angles given, the third is uniquely determined, ensuring that there will be only one possible triangle that can be constructed under these conditions with a fixed side between the two known angles.
Since the sides of a triangle are determined by their angles, the side-angle-side (SAS) condition is satisfied when two angles and the included side are known. This guarantees the uniqueness of the triangle. The given side of 3 feet, being between the two known angles, completes this condition.