Question

list the side lengths of $\triangle abc$ in order from shortest to longest, given that $m\angle c = 35^\circ$, $m\angle a = 30^\circ$, and $m\angle b = 115^\circ$. \\(\square < \square < \square\\) submit

Explanation:

Step1: Recall triangle side-angle rule

In any triangle, the length of a side is proportional to the measure of its opposite angle: the smallest angle corresponds to the shortest side, and the largest angle corresponds to the longest side.

Step2: Match angles to opposite sides

• $\angle A = 30^\circ$, opposite side $BC$
• $\angle C = 35^\circ$, opposite side $AB$
• $\angle B = 115^\circ$, opposite side $AC$

Step3: Order sides by angle size

Since $30^\circ < 35^\circ < 115^\circ$, the opposite sides follow the same order.

Answer:

$BC < AB < AC$