Question

list the side lengths from shortest to longest for each diagram.
①
②

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 LKM

In \(\triangle LKM\), the third angle \(\angle M=180^{\circ}-(28^{\circ} + 118^{\circ})=34^{\circ}\). Since \(28^{\circ}<34^{\circ}<118^{\circ}\), the sides from shortest to longest are \(l,k,m\).

Step3: Analyze angles in the second - figure

In the second figure, consider the angles at the vertices. The smallest angle is \(27^{\circ}\), the next is \(64^{\circ}\), then \(67^{\circ}\), and the largest is \(79^{\circ}\). The side opposite the \(27^{\circ}\) angle is \(o\), the side opposite the \(64^{\circ}\) angle is \(c\), the side opposite the \(67^{\circ}\) angle is \(b\), and the side opposite the \(79^{\circ}\) angle is \(d\). Also, side \(e\) is the hypotenuse of the right - angled part and is the longest among all. So the sides from shortest to longest are \(o,c,b,d,e\).

Answer:

a. \(l,k,m\)
b. \(o,c,b,d,e\)