Question

list the side lengths of $\triangle tuw$ in order from shortest to longest.

Explanation:

Step1: Find ∠UTW

∠UTW = 180° - 110° = 70°

Step2: Find ∠U

∠U = 180° - 70° - 30° = 80°

Step3: Match sides to angles

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

• Smallest angle: 30° (∠W), opposite side $UW$
• Middle angle: 70° (∠UTW), opposite side $UW$ correction: opposite side $TU$
• Largest angle: 80° (∠U), opposite side $TW$

Answer:

$UW < TU < TW$