Question

list the side lengths of δfgh in order from shortest to longest, given that m∠h = 38°, m∠g = 105°, and m∠f = 37°. \\(\square < \square < \square\\) submit

Explanation:

Step1: Recall Angle-Side Relationship

In a triangle, the larger the angle, the longer the side opposite to it. So we first order the angles by measure.
Given angles: \( m\angle F = 37^\circ \), \( m\angle H = 38^\circ \), \( m\angle G = 105^\circ \). Order of angles from smallest to largest: \( \angle F < \angle H < \angle G \).

Step2: Identify Opposite Sides

• Side opposite \( \angle F \) is \( GH \).
• Side opposite \( \angle H \) is \( FG \).
• Side opposite \( \angle G \) is \( FH \).

Step3: Order Sides by Angle Relationship

Since angle order is \( \angle F < \angle H < \angle G \), their opposite sides follow the same order. So \( GH < FG < FH \).

Answer:

\( GH \) \( < \) \( FG \) \( < \) \( FH \)