In triangle ABC, the greatest angle is ∠ABC (104°), with other angle measures at 30° and 46°. The smallest angle, opposite the shortest side, is ∠ACB (30°). Thus, the angle-side relationships in the triangle are established.
In triangle ABC, the greatest angle is ∠ABC, measuring 104 degrees. The other angle measures are 30 and 46 degrees. According to the Triangle Inequality Theorem, the smallest angle is opposite the shortest side. To identify the smallest side, compare the angle measures.
Since ∠ABC is the greatest angle, the side opposite ∠ABC is the longest. Therefore, the smallest angle, opposite the shortest side, must be ∠ACB. Thus, ∠ACB measures 30 degrees, ∠BCA measures 46 degrees, and ∠ABC measures 104 degrees. The side opposite ∠ACB is the shortest side in this triangle.