Question

question 2 (4 points)knowing what you know about the sides of triangles and their corresponding angles, put the sides (side a, side b, side c) in order from smallest to largest, and explain how you know. (3 points)

Explanation:

Step1: Find missing angle at C

The sum of angles in a triangle is $180^\circ$.
$\angle C = 180^\circ - 91^\circ - 30^\circ = 59^\circ$

Step2: Match sides to opposite angles

• Side a is opposite $\angle A = 91^\circ$
• Side b is opposite $\angle B = 30^\circ$
• Side c is opposite $\angle C = 59^\circ$

Step3: Order sides by angle size

In a triangle, the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle.
Smallest angle ($30^\circ$) → shortest side (side b); middle angle ($59^\circ$) → middle side (side c); largest angle ($91^\circ$) → longest side (side a)

Answer:

Side b < Side c < Side a

The side opposite the smallest interior angle of a triangle is the shortest side, and the side opposite the largest interior angle is the longest side. After calculating the missing angle at $C$ as $59^\circ$, we match each side to its opposite angle: side b (opposite $30^\circ$), side c (opposite $59^\circ$), side a (opposite $91^\circ$), then order them from smallest to largest.