To solve this triangle inequality problem, we can use the fact that in a triangle, the side opposite a larger angle is longer than the side opposite a smaller angle.

Step-by-step analysis:

1. Angles provided:

   • $\angle R = 35^\circ$
   • $\angle T = 75^\circ$
   • $\angle A = 180^\circ - (35^\circ + 75^\circ) = 70^\circ$

2. Sides are related to opposite angles:

   • The side opposite the largest angle ($75^\circ$) is the longest.
   • The side opposite the next largest angle ($70^\circ$) is the second longest.
   • The side opposite the smallest angle ($35^\circ$) is the shortest.

3. Opposite side names:

   • $\angle R = 35^\circ$: Opposite side is $TA$.
   • $\angle T = 75^\circ$: Opposite side is $RA$.
   • $\angle A = 70^\circ$: Opposite side is $RT$.

Order of sides (from largest to smallest):

1. $RA$ (opposite $75^\circ$)
2. $RT$ (opposite $70^\circ$)
3. $TA$ (opposite $35^\circ$)

Final Answer:

$RA > RT > TA$

Would you like further explanation or details? Here are some related questions for practice:

1. How do you calculate unknown angles in a triangle?
2. Why is the longest side always opposite the largest angle in a triangle?
3. How can this principle be applied to obtuse or right triangles?
4. What are the triangle inequality rules for side lengths?
5. How can trigonometric ratios (sine, cosine) confirm side relationships in a triangle?

Tip: Always remember that angle-side relationships in triangles are proportional.