Question

list the sides of the triangle in order from shortest to longest.
triangle fgh with angles at f: 61°, at g: 59°, sides fg, gh, fh to be ordered.

Explanation:

Step1: Find the measure of angle \( H \)

The sum of angles in a triangle is \( 180^{\circ} \). Let \( \angle H=x \). Then \( 61^{\circ}+59^{\circ}+x = 180^{\circ} \). So \( x=180^{\circ}-(61^{\circ} + 59^{\circ})=60^{\circ} \).

Step2: Recall the side - angle relationship

In a triangle, the side opposite the smaller angle is shorter.

• Opposite \( \angle G = 59^{\circ}\) is side \( FH \)
• Opposite \( \angle H=60^{\circ}\) is side \( FG \)
• Opposite \( \angle F = 61^{\circ}\) is side \( GH \)

Answer:

\(\overline{FH},\overline{FG},\overline{GH}\)