Question

how do I know where to place the sides in order from longest (at the top) to shortest (at the bottom)?

Answer 1

DF

EF

DE

Step-by-step explanation:

To know the order of the sides, we need to identify all three interior angles.

So, to know the missing angle, we will apply that the sum of all interior angles of a triangle is equal to 180°. It means that:

∠D + ∠E + ∠F = 180

∠D + 61 + 59 = 180

∠D + 120 = 180

∠D = 180 - 120

∠D = 60°

Now, the relation between every side and its opposite angle is proportional. It means that if the greatest angle is E, the longest side is the opposite one or DF.

So, the ordered angles and sides are:

∠E = 61° -----> DF

∠D = 60° -----> EF

∠F = 59° -----> DE

Therefore, the sides in the order form longest to shortest are:

DF

EF

DE