Question

which dimensions can create more than one triangle? three sides measuring 7 m, 10 m, and 12 m three angles measuring 75°, 45°, and 60° three sides measuring 3 cm, 4 cm, and 5 cm three angles measuring 40°, 50°, and 60°

Explanation:

When given three side lengths (as in the cases of three sides measuring 7 m, 10 m, and 12 m or three sides measuring 3 cm, 4 cm, and 5 cm), a unique triangle is determined by the SSS (Side - Side - Side) congruence criterion. When given three angles (as in the case of three angles measuring 75°, 45°, and 60°), infinitely many similar triangles (triangles with the same shape but different sizes) can be created. For three angles measuring 40°, 50°, and 60°, \(40 + 50+60=150
eq180\), so no triangle can be formed.

Answer:

three angles measuring \(75^{\circ}\), \(45^{\circ}\), and \(60^{\circ}\)