Image shows a triangle with 3 angles. Angle J = 57 degrees. Angle K = 78 degrees. Angle L = 45 degrees. List the sides in order from shortest to longest (Line LK, Line JK, Line LJ)

1 answer

To determine the order of the sides from shortest to longest, we need to analyze the angles and their relationships within the triangle.

Given that angle J is 57 degrees, angle K is 78 degrees, and angle L is 45 degrees, we can apply the triangle angle sum property:

Angle J + Angle K + Angle L = 180 degrees.

57 degrees + 78 degrees + 45 degrees = 180 degrees.

Therefore, the given angles form a valid triangle.

Now let's analyze the relationship between the angles and the sides:

- The longest side is opposite the largest angle in a triangle.
- The shortest side is opposite the smallest angle.

Therefore, to determine the order of the sides, we need to compare the sizes of the angles.

Angle J = 57 degrees
Angle L = 45 degrees
Angle K = 78 degrees

Comparing the sizes of the angles, we can determine the order of the sides:

The side opposite angle L (45 degrees) will be the shortest side.
The side opposite angle J (57 degrees) will be the next longer side.
The side opposite angle K (78 degrees) will be the longest side.

Thus, the sides in order from shortest to longest are:
Line LK, Line LJ, Line JK.