Question

list the side lengths of δqrs in order from shortest to longest, given that m∠s = 98°, m∠q = 46°, and m∠r = 36°. □ < □ < □ submit

Explanation:

Step1: Match angles to opposite sides

In $\Delta QRS$:

• $\angle R$ (36°) is opposite $\overline{QS}$
• $\angle Q$ (46°) is opposite $\overline{RS}$
• $\angle S$ (98°) is opposite $\overline{QR}$

Step2: Order angles from smallest to largest

$36^\circ < 46^\circ < 98^\circ$, so $m\angle R < m\angle Q < m\angle S$

Step3: Relate to side lengths

In a triangle, shorter sides are opposite smaller angles.

Answer:

$\overline{QS} < \overline{RS} < \overline{QR}$