To determine the order of the side lengths of a triangle given its angles, we use the following principle:

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

Step-by-step reasoning:

1. The triangle has the following angles:

   • ∠A = 65°
   • ∠B = 45°
   • ∠C = 70°

2. Compare the angles:

   • The largest angle is ∠C = 70°.
   • The next largest angle is ∠A = 65°.
   • The smallest angle is ∠B = 45°.

3. The side lengths are proportional to the size of the angles they face:

   • The side opposite ∠C is AB.
   • The side opposite ∠A is BC.
   • The side opposite ∠B is AC.

4. Order the sides from least to greatest:

   • AC (smallest, opposite 45°)
   • BC (middle, opposite 65°)
   • AB (largest, opposite 70°)

Final Answer:

The side lengths in order from least to greatest are: AC, BC, AB.

Let me know if you need further clarification! Here are 5 related questions for practice:

1. How do you calculate the side lengths of a triangle using the Law of Sines?
2. What is the sum of the interior angles of any triangle?
3. How can you determine whether a triangle is acute, right, or obtuse?
4. What is the relationship between angles and sides in a triangle?
5. How do you use the Law of Cosines to find missing sides of a triangle?

Tip: Always remember, the largest angle in a triangle corresponds to the longest side, and the smallest angle corresponds to the shortest side.