Question

order the side lengths $hi$, $ij$, and $jh$ from least to greatest.
(note that the figure is not drawn to scale.)

Explanation:

Step1: Find ∠J

The sum of angles in a triangle is $180^\circ$.
$\angle J = 180^\circ - 55^\circ - 44^\circ = 81^\circ$

Step2: Match sides to opposite angles

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

• $\angle H = 44^\circ$ (smallest) → opposite side $IJ$
• $\angle I = 55^\circ$ → opposite side $JH$
• $\angle J = 81^\circ$ (largest) → opposite side $HI$

Answer:

$IJ < JH < HI$