Question

list the side lengths of $\triangle ghi$ in order from shortest to longest, given that $m\angle g = 64^\circ$, $m\angle h = 43^\circ$, and $m\angle i = 73^\circ$.\
\\(\square < \square < \square\\)

Explanation:

Step1: Match sides to opposite angles

In $\triangle GHI$:

• Side opposite $\angle G$: $HI$
• Side opposite $\angle H$: $GI$
• Side opposite $\angle I$: $GH$

Step2: Order angles from smallest to largest

$m\angle H = 43^\circ < m\angle G = 64^\circ < m\angle I = 73^\circ$

Step3: Order sides by opposite angles

The shortest side is opposite the smallest angle, and the longest side is opposite the largest angle.

Answer:

$GI < HI < GH$