Question

ordering sides list the sides in order from shortest to longest. 15. e 30° f d

Explanation:

Step1: Find the third angle

In a triangle, the sum of angles is \(180^{\circ}\). Given \(\angle E = 30^{\circ}\) and \(\angle D=90^{\circ}\), then \(\angle F=180^{\circ}-30^{\circ}-90^{\circ}=60^{\circ}\).

Step2: Apply the side - angle relationship

In a triangle, the side opposite the smaller angle is shorter. The order of angles from smallest to largest is \(\angle E(30^{\circ})<\angle F(60^{\circ})<\angle D(90^{\circ})\).
The side opposite \(\angle E\) is \(DF\), the side opposite \(\angle F\) is \(DE\), and the side opposite \(\angle D\) is \(EF\).

Answer:

\(DF < DE < EF\)