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 at B

In a triangle, the sum of angles is $180^\circ$. So, $\angle B = 180^\circ - 44^\circ - 89^\circ = 47^\circ$.

Step2: Relate angles to sides

In a triangle, the larger the angle, the longer the opposite side.

• Opposite $\angle A$ ($44^\circ$) is $BC$.
• Opposite $\angle B$ ($47^\circ$) is $AC$.
• Opposite $\angle C$ ($89^\circ$) is $AB$.

Order of angles: $44^\circ < 47^\circ < 89^\circ$ (i.e., $\angle A < \angle B < \angle C$). So, the order of opposite sides: $BC < AC < AB$.

Answer:

$BC < AC < AB$