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)
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.