Question

△gef
∠g = 44°, ∠e = 33°, ∠f = 103°
arrange the sides from shortest to longest based on their lengths.
none of these
\overline{ge}, \overline{ef}, \overline{gf}
\overline{ef}, \overline{gf}, \overline{ge}
\overline{gf}, \overline{ef}, \overline{ge}

Explanation:

Step1: Recall the triangle side - angle relationship

In a triangle, the larger the angle, the longer the side opposite it.

Step2: Identify the sides opposite the given angles

In \(\triangle GEF\), side \(EF\) is opposite \(\angle G\), side \(GF\) is opposite \(\angle E\), and side \(GE\) is opposite \(\angle F\).

Step3: Compare the angles

We have \(\angle G = 44^{\circ}\), \(\angle E=33^{\circ}\), \(\angle F = 103^{\circ}\). Since \(33^{\circ}<44^{\circ}<103^{\circ}\), i.e., \(\angle E<\angle G<\angle F\).

Step4: Arrange the sides

By the side - angle relationship, the side opposite the smaller angle is shorter. So, \(GF\) (opposite \(\angle E\)) \(

Answer:

\(\overline{GF},\overline{EF},\overline{GE}\)