Question

list the side lengths of δabc in order from shortest to longest, given that m∠c = 35°, m∠a = 30°, and m∠b = 115°. \\(\square < \square < \square\\) submit

Explanation:

Step1: Recall triangle side-angle relationship

In any triangle, the shortest side is opposite the smallest angle, and the longest side is opposite the largest angle.

Step2: Match angles to opposite sides

• $m\angle A = 30^\circ$ (smallest angle) $

ightarrow$ opposite side $BC$

• $m\angle C = 35^\circ$ (middle angle) $

ightarrow$ opposite side $AB$

• $m\angle B = 115^\circ$ (largest angle) $

ightarrow$ opposite side $AC$

Step3: Order sides by angle size

Arrange sides from shortest to longest based on the corresponding angles.

Answer:

$BC < AB < AC$