In the provided image, we are tasked with ordering the sides of the triangle from shortest to longest. The triangle has the following angles labeled:

• Angle $\angle K = 40^\circ$
• Angle $\angle J = 70^\circ$
• Angle $\angle L = 70^\circ$

Step-by-step Solution:

1. Triangle Properties:

   • The sum of the angles in any triangle is $180^\circ$. Here, $40^\circ + 70^\circ + 70^\circ = 180^\circ$, so this is a valid triangle.
   • The length of a side is proportional to the sine of the opposite angle. Larger angles correspond to longer sides.

2. Angles and Opposite Sides:

   • Side $\overline{LJ}$ is opposite $\angle K = 40^\circ$.
   • Side $\overline{LK}$ is opposite $\angle J = 70^\circ$.
   • Side $\overline{KJ}$ is opposite $\angle L = 70^\circ$.

3. Order the Sides:

   • Since $\angle K < \angle J = \angle L$, the order of the sides (from shortest to longest) is: $\overline{LJ} < \overline{LK} = \overline{KJ}$

Final Answer:

The sides in order from shortest to longest are:

A) $\overline{LJ}, \overline{LK}, \overline{KJ}$.

Would you like further clarification or a breakdown of why the angles determine the side lengths? Here are some related questions you might find helpful:

1. How do you calculate side lengths using the sine rule?
2. Why do equal angles imply equal opposite sides in a triangle?
3. What other triangle properties can we deduce from angles alone?
4. How can we classify triangles based on angle properties?
5. What happens if all three angles are different? How does that affect the side lengths?

Tip: Always check the sum of angles to ensure the problem is dealing with a valid triangle!