Question

order the side lengths ab, bc, and ca from least to greatest. (note that the figure is not drawn to scale.)

Explanation:

Step1: Find angle B

Use the angle - sum property of a triangle ($\angle A+\angle B+\angle C = 180^{\circ}$). So, $\angle B=180^{\circ}-(86^{\circ}+41^{\circ}) = 53^{\circ}$.

Step2: Recall the side - angle relationship

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

Step3: Order the sides

Since $41^{\circ}<53^{\circ}<86^{\circ}$, the side opposite $\angle A$ is $BC$, the side opposite $\angle B$ is $AC$, and the side opposite $\angle C$ is $AB$. So, $BC < AC < AB$.

Answer:

$BC < CA < AB$