List the side lengths of △GHI in order from smallest to largest, given that m∠G=14s+17°, m∠H=70s–37°, and m∠I=89s+27°.

To solve this problem, we first need to understand that the size of an angle in a triangle is directly related to the length of the opposite side. The larger the angle, the longer the side.

Step 1: Solve for 's' in each of the given angle measures.

m∠G = 14s + 17° m∠H = 70s - 37° m∠I = 89s + 27°

Since the sum of the angles in a triangle is 180°, we can set up the following equation:

14s + 17 + 70s - 37 + 89s + 27 = 180

Combine like terms:

173s + 7 = 180

Subtract 7 from both sides:

173s = 173

Divide both sides by 173:

s = 1

Step 2: Substitute s = 1 back into the original angle measures to find the actual measures of the angles.

m∠G = 14(1) + 17 = 31° m∠H = 70(1) - 37 = 33° m∠I = 89(1) + 27 = 116°

Step 3: List the side lengths in order from smallest to largest based on the angle measures. The side opposite the smallest angle will be the shortest, and the side opposite the largest angle will be the longest.

So, the order of the side lengths from smallest to largest is: GH, GI, HI.