Question

Which dimensions can create only one unique triangle?
three angles measuring 75 degrees, 45 degrees, and 50 degrees
three sides measuring 14 m, 11 m, and 18 m
three angles measuring 40 degrees, 50 degrees, and 60 degrees
three sides measuring 3 cm, 4 cm, and 8 cm

Answer 1

Only the three sides 14 m, 11 m, and 18 m.

Reasoning:
- A valid triangle must have angle measures summing to 180°. 75°+45°+50° = 170° (not 180°) and 40°+50°+60° = 150° (not 180°), so those angle sets cannot form any triangle.
- A set of three side lengths forms a unique triangle exactly when they satisfy the triangle inequalities. 14, 11, and 18 satisfy 11+14>18, 14+18>11, and 11+18>14, so they form one unique triangle (SSS determines a congruent triangle).
- 3, 4, and 8 fail the triangle inequality (3+4=7 ≤ 8), so they cannot form a triangle.