Question

1. use patterns and structure a stage manager must use tape to outline a triangular platform on the set. order the sides of the platform from longest to shortest. (triangle qsr with angle at q: 63°, angle at r: 57°)

Explanation:

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

The sum of angles in a triangle is \( 180^{\circ} \). Let \( \angle S=x \). Then \( x + 63^{\circ}+57^{\circ}=180^{\circ} \). So \( x=180^{\circ}-(63^{\circ} + 57^{\circ})=60^{\circ} \).

Step2: Apply the angle - side relationship in a triangle

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

• Opposite \( \angle Q = 63^{\circ} \) is side \( SR \)
• Opposite \( \angle R=57^{\circ} \) is side \( SQ \)
• Opposite \( \angle S = 60^{\circ} \) is side \( QR \)

Since \( 63^{\circ}>60^{\circ}>57^{\circ} \), the order of the sides from longest to shortest is based on the angles opposite them.

Answer:

\( SR>QR>SQ \)