Question

list the sides from shortest to longest in abc. a. ab, bc, ac b. bc, ac, ab c. ac, bc, ab d. not enough information

Explanation:

Step1: Find angle B

The sum of angles in a triangle is 180°. So, $\angle B=180^{\circ}-\angle A - \angle C=180^{\circ}-63^{\circ}-50^{\circ}=67^{\circ}$.

Step2: Recall angle - side relationship

In a triangle, the side opposite the smallest angle is the shortest and the side opposite the largest angle is the longest.

Step3: Identify smallest and largest angles

The smallest angle is $\angle C = 50^{\circ}$, the middle - sized angle is $\angle A=63^{\circ}$, and the largest angle is $\angle B = 67^{\circ}$.

Step4: Match sides to angles

The side opposite $\angle C$ is $\overline{AB}$, the side opposite $\angle A$ is $\overline{BC}$, and the side opposite $\angle B$ is $\overline{AC}$. So, the order of sides from shortest to longest is $\overline{AB},\overline{BC},\overline{AC}$.

Answer:

A. $\overline{AB},\overline{BC},\overline{AC}$