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

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

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

Answer

Explanation:

Step1: Sum angles to 180°

$$(w+62) + 71w + 46w = 180$$

Step2: Simplify the equation

$$118w + 62 = 180$$

Step3: Solve for w

$$118w = 180 - 62 = 118 \implies w=1$$

Step4: Calculate each angle

  • $\angle T = 1+62 = 63^\circ$
  • $\angle S = 71\times1 = 71^\circ$
  • $\angle U = 46\times1 = 46^\circ$

Step5: Match sides to opposite angles

Side opposite $\angle U$: $ST$ Side opposite $\angle T$: $SU$ Side opposite $\angle S$: $TU$ Order angles: $46^\circ < 63^\circ < 71^\circ$, so sides follow the same order.

Answer:

$ST < SU < TU$