Question

list the side lengths of △abc in order from shortest to longest, given that m∠c = 76° and m∠b = 49°. \\(\square < \square < \square\\) submit

Explanation:

Step1: Find $m\angle A$

The sum of angles in a triangle is $180^\circ$.
$m\angle A = 180^\circ - m\angle B - m\angle C = 180^\circ - 49^\circ - 76^\circ = 55^\circ$

Step2: Match angles to opposite sides

In a triangle, the shortest side is opposite the smallest angle, and the longest side is opposite the largest angle:

• Smallest angle: $m\angle B=49^\circ$, opposite side $\overline{AC}$
• Middle angle: $m\angle A=55^\circ$, opposite side $\overline{BC}$
• Largest angle: $m\angle C=76^\circ$, opposite side $\overline{AB}$

Step3: Order sides from shortest to longest

Arrange the sides based on the angle order.

Answer:

$AC < BC < AB$