Question

1. list the side lengths from shortest to longest for each diagram.

a.
b.

Explanation:

Step1: Recall angle - side relationship in a triangle

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

Step2: Find the third angle in triangle a

The sum of angles in a triangle is 180°. In triangle a, if two angles are 28° and 118°, the third angle is $180-(28 + 118)=34°$. The angles are 28°, 34°, 118°. The sides opposite these angles are l, k, m respectively. So the order of side - lengths from shortest to longest is l, k, m.

Step3: Find the angles in triangle b

In triangle b, we have angles 27°, 63°, 79°, 180-(27 + 63+79)=11°. The sides opposite these angles are a, b, c, d, e respectively. The order of side - lengths from shortest to longest is e, a, b, c, d.

Answer:

a. l, k, m
b. e, a, b, c, d