Question

list the side lengths of △abc in order from shortest to longest.

Explanation:

Step1: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. So, $(y + 48^{\circ})+(3y)+(y + 52^{\circ})=180^{\circ}$.
Combining like - terms: $5y+100^{\circ}=180^{\circ}$.
Subtract $100^{\circ}$ from both sides: $5y=180^{\circ}-100^{\circ}=80^{\circ}$.
Divide both sides by 5: $y = 16^{\circ}$.

Step2: Find the measure of each angle

Angle $B=y + 48^{\circ}=16^{\circ}+48^{\circ}=64^{\circ}$.
Angle $C = 3y=3\times16^{\circ}=48^{\circ}$.
Angle $A=y + 52^{\circ}=16^{\circ}+52^{\circ}=68^{\circ}$.

Step3: Use the angle - side relationship in a triangle

In a triangle, the side opposite the smallest angle is the shortest and the side opposite the largest angle is the longest.
Since $\angle C<\angle B<\angle A$, the side opposite $\angle C$ is $AB$, the side opposite $\angle B$ is $AC$, and the side opposite $\angle A$ is $BC$.
So, $AB

Answer:

$AB