Question

let the sides in order from shortest (at the bottom) be: d e f 36° 57° a

Explanation:

Step1: Find angle \(a\)

The sum of angles in a triangle is \(180^{\circ}\). So \(a=180^{\circ}-36^{\circ} - 57^{\circ}=87^{\circ}\).

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: Order the sides

Since \(36^{\circ}<57^{\circ}<87^{\circ}\), the side opposite \(36^{\circ}\) is the shortest, the side opposite \(57^{\circ}\) is the middle - length side, and the side opposite \(87^{\circ}\) is the longest. The side opposite \(36^{\circ}\) is \(DF\), the side opposite \(57^{\circ}\) is \(DE\), and the side opposite \(87^{\circ}\) is \(EF\). So the order from shortest to longest is \(DF, DE, EF\).

Answer:

\(DF, DE, EF\)